Do you get to make your own character or do you have to choose from a premade character at the start of the game?

Just wanted to know this before I buy the game.

In the vanilla game there are three characters to choose from, though you can adjust their stats at the beginning.

If you use the Gentlemen of Fortune mod (you can find it at Mod Database), there are many to choose from. And you can adjust the stats at the beginning for each.

I know it's year old, but nobody answer this one, you can edit HeroDescribe.txt files name, and number of model that game had it, it's take little work to find number for model looking, and simple rename whatever you like.

Main folder/RESOURCE/INI/texts/russian/HeroDescribe.txt

I like best personal, but might end up look same as npc ingame
heroFace_1 {22}
heroModel_1 {officer_5,officer_5_cirass,officer_5_cirass1,officer_5_cirass2,officer_5_cirass3,officer_5_cirass4}

Does CoAS have the option to play a female character, or would I need to buy Caribbean Tales instead/as well to play as a lady pirate?

There are three characters to choose from, all three males.
For a female pirate you'll need to use a mod. There are several major mods available at Mod Database.