Wowzers!
I'll try my shot at some IDs! Be sure to open the pictures as I attached numbers with the ones I IDed/attempted to ID.
#1 + #3. Same cactus actually! They're baby Echinocactus grusonii 'Golden Barrel' (they look so different as adults).
#2. Mammillaria hahniana 'Old Lady Cactus'
The more "naked" one up front looks like a Mammillaria to me, I'm just not sure which one.
4. Parodia magnifica 'Balloon Cactus'
5. Okay, this one I'm not 100% sure so you may have to get a second opinion (it was a little hard to see it's spines), but I believe it's Mammillaria spinosissima 'Red Headed Irishman' Some of their spines vary from cactus to cactus. My Mother has one that's more half white/half red and some are very red all the way down the spine.