Can I bring these items on an airplane?

Yup, all are fine as long as they are not in your carry-on. Although it's not required, I'd suggest putting them in a plastic bag (like a large Ziplock) in case something breaks open. That way you won't open your suitcase to find shampoo all over your clothes!

Yes, as long as they are in your suitcase and not in your carry on.

If you wanted to put these items in your carry on, they would have to be placed in containers of roughly 3.4 oz each and then in a quart-sized ziplock bag.

not in your carry on unless you follow the 3-1-1 rule which is...

-3.4oz (100ml) containers or smaller

-all containers must be placed in a 1 quart size clear plastic zip top baggie

-only 1 baggie per person

-during security you must take out the baggie and place it in a bin provided to you for it to go through the x-ray machine

you can however put them in your checked luggage just as it is.

most of it you can take but u can only take the eye contact solution if its less then 3 ounces. So my grandma took lotion more ten 3 ounces as her carry on the didn't let her take it with her and they threw it away. also the makeup stuff less then 3 ounces just put the eye contact solution in ur luggage

Yes you can bring them just make sure to wrap them in a plastic bag so in case it explodes it won't get messy (same goes for nail polish)

All of those are okay if you do not carry them on :)