I applaud you for wanting to learn how to potentially improve your AIS station. As others have commented, your questions can yield a response the size of a textbook but here are a few pointers to get you started. Perhaps some experimenting will lead you to post further questions for this forum which will help others with their understanding as well.
You didn't give a detailed description of your station configuration so for the purposes of this answer, I will assume that you have your SDR connected to a 50 ohm coax cable that heads towards your antenna where it is plugged into the output of the preamp. On the input side of your preamp you have a 75 ohm to 300 ohm balun connected to your horizontally strung folded dipole antenna. If this in inaccurate, correct me with a comment in response to this answer and I will adjust my answer as appropriate.
Receiver Noise Level
Your SDR generates some noise within its own electronics. While the designers take care to reduce the power and spectrum of this noise, it cannot be entirely eliminated. In fact, even a simple resistor will generate a small level of noise (called Johnson-Nyquist noise) that varies with its temperature.
The noise generated by the SDR is often called the noise floor of the receiver. You can roughly measure this noise by removing the coax cable from your SDR and substituting a 50 ohm, non-inductive resistor (any wattage will do) across the input of your receiver. Then observe that there are no signals on your SDR display but only noise "bubbling" on the bottom of the spectrum. Take note of where the peaks of this noise land on the spectrum display. Your display will typically show dBm as the vertical scale. This is a relative indication of the noise power. Record this reading for future reference.
This is really only an approximation because your computer is connected to the SDR and it is probably contributing some level of noise itself. But since they are both required to make a functioning receiver, you can practically view this as the noise floor of your receiver.
Your Coax Cable
Normally your terminated coax cable (or any transmission line) should not, on its own, pick up any signals. But life is not perfect so it is always good to check out if your coax cable is doing its job. To do this, reconnect the coax cable to your SDR and disconnect the far end of the cable from the preamp and substitute your 50 ohm resistor for the preamp. Power down the preamp.
Recheck your waterfall display to make certain there are no discernible signals present and that your noise floor is about the same as what you previously measured. If you spot any significant changes, start checking your coax for bad connections or for a break somewhere in the coax.
A preamp will generate some of its own noise. This is unavoidable although the higher the quality of the preamp, generally the lower the contributed noise. You can test the amount of noise your preamp contributes by reconnecting the preamp to the coax cable,powering it up, and placing your resistor on the input of the preamp where the antenna would normally connect. The unused UHF input of your preamp should always be terminated with a resistor (300 or 75 ohm as appropriate) to limit additional noise contribution.
With the inputs of the preamp terminated with resistors, remeasure the noise floor of your receiver. Any increase in noise is attributable to the preamp.
You stated that you are using a folded dipole for reception. Normally these are used in a horizontal configuration. The ships that are transmitting their AIS signals have vertically polarized antennas. This cross polarization of antennas can easily result in a 10-20 dB loss in received signal strength. While you could restring your dipole in a vertical fashion and carefully route the feedline away in a perpendicular direction, you would probably have much better success with a simple vertical antenna. At 162 MHz, a quarter wave, ground plane, vertical antenna is only ~1.5 feet (44 cm) tall. A quarter wave sleeve antenna would also make a very good choice. You could also construct a slightly more sophisticated vertical antenna that gives additional gain.
Since the loss of this cross polarization could be greater than the gain of your preamp, it would be worth experimenting with a different antenna. You may find that you can eliminate the preamp.
Filters and Noise
There are many sources of "noise". Our atmosphere and the galaxies around us contribute noise of their own. Most of this noise stays well below 100 MHz.
The most troubling noise to those of us using receivers is man-made noise. This constantly increasing noise floor comes from LED power supplies, computers, washers, dryers, furnaces, routers, wall warts, etc. In general though, most of this noise drops off below 100 MHz or so. There can certainly be man made noise above 100 MHz but it is not common nor generally dominant.
Then there are interfering signals. These generally originate from intentionally generated RF signals. It could be the signal itself that interferes or it can be a mixing of these signals ("intermod", short for inter-modulation) that cause the interference. These types of signals are generally not considered "noise" since they result in a very narrow band signal. These would generally appear as narrow spikes on your SDR display.
Intentionally generated signals can also create noise that can interfere with your desired signals. But the services that are operating around your intended received frequency are fairly tightly regulated by the FCC and are likely not to exhibit these characteristics. With that being said, I have been called into situations where the regulated transmitter was indeed "dirty". There are also less common effects where a tower or other structure generates the offending signal - often called a "rusty nail" problem. But this is a digression from your question.
Interfering signals can also be generated by your preamp when it is overloaded with a strong signal even if it is not on the same frequency. The preamp will internally create other signals that would otherwise not be present. You can detect this by bypassing and powering down the preamp and checking the waterfall display again. If the undesired spikes are still present but of lower signal strength, it is not your preamp that is causing it - it is simply amplifying an existing signal. If the offending spike is completely gone, then you may begin to suspect your preamp.
Adding a filter in advance of your preamp will reduce the bandwidth that your preamp will amplify and this can reduce interfering signals. But a filter will not reduce noise or interfering signals that are already present on the frequency in which you are interested. A filter will always introduce some additional loss of a few dBs but if the filter is warranted, this is usually a reasonable trade-off.
After experimenting with the other factors described, if you feel a filter is warranted, you will find several on-line filter engineering programs or you can download free programs like Elsie to help you design a filter. There are many experienced engineers and practitioners on this site that can help with pointers if you get stuck.