Beating bosses is one form, madman's knowledge is another. Aiding in coop can also give insight as well but ill get into that at the bottom. The doll will be who you talk to to level up yes, she will always be awake if you have 1 or more insight, you can also talk to her to learn some more stuff about the world, and try to do some emotes in front of her as well!

Pick whatever weapon you prefer i will tell you this, eventually you will have the opportunity to have them all.

Armor is worthwhile depending on the current area you are in, eventually you will find areas that have alot of enemies with poison damage. In this case you should find some high poison resist armor which will be offered to you eventually (trying to keep this spoiler free!) Always pay attention to the stats some have higher physical defense than others the numbers in the middle box when equipping armor will show you. Weapons will also be purchasable down the line when you get drops in the form of badges.

As for your Snorlax nemesis he is a great opportunity to practice parrying on, unlock the shortcut next to him for quick access to the lantern and just try parrying. In his case when he is at the peak of his axe swing, shoot. He is fast so you wanna be quick on the draw for him. Or if you really want take your axe, press the L1 to extend it and practice holding R2 for your charge attack and send him flying! And always stay on your toes and manage your stamina, 1 extra hit is not worth it if it leaves your stamina bar empty and you can't dodge the incoming attack. Remember this game is fast paced so you always want to be 1 step ahead.

You can play with people online, eventually you will find 3 different bells which are also available via the insight mechanic. Once you have 1 insight point you can get 1 of those bells head to that doll and some of it will be explained for you. If you wan't more details let me know, i'd avoid the wiki only because its spoiler-city!