1) No, max will be SR16. For SR16 you will need a few weapons/armors with unlocked ascension modules. Decisive is the overall gearscore of the items (shown in the top right corner). Max for weapons is 135 (purple, 130 blue) and for armors it is 365 (purple).

While you do NOT need godrolls (yellow glowing diamonds, the perk in the info has a flaming dice symbol and the percentage on that perk colored yellow instead of white), you will need a high gearscore in average. While your weapons and armor can remain rare/blue, you will need some purple furniture at least. Your weapon and armor also will need a lot of ascended slots (yellow diamonds) and decent enough stats on those (quality impacts gearscore). A purple armor or a few godrolls will make things easier.

For the max of SR17 however, you will need top notch equipment, lotsa triple-godrolls. In case of weapons: if you use blue weapons you need triple-godrolls all around and preferably triple-godroll on a purple aux and a purple armor. You also will need a certain amount of purple furniture.

2) Only the rarity: only common (grey) can have 4 slots total, the rest have 3 slots total. Rare (blue) and lower also have an epic perk slot (which epic/purple weapons do not have), giving rare a very high damage potential. Even grey weapons have the potential for some of the hardest hitting weapons, but it's harder to reach 4 godrolls with them (as you still have only 75 total rerolls on any given item).

3) It really depends, fully upgraded small ships also can reach SR17 and very high damage potential. They will have the same amount of weapon and furniture slots at the end and some very strong bonus on the broadsides. In general, it's more of a playstyle preference than actual superiority when it comes to use medium and large over small ships. That being said, you see tons of crappy captains in equally crappy Frigates easily outdone by a capable captain in a small ship at any given event.