If you look through older threads, you'll see that your not the first to come up with this. Asper made a version without the sifting, and he said it was balanced, just unfun. The best version I saw was "Deposit" which was Asper's with a once per turn. I'd suggest ditching this and working on your much more unique ideas.
6 might work, test it at 6 as well as five. I like it as a card though.
Seems a bit weak at first. After reading it over my only suggestion is to make the gaining optional, or to make it an attack.
Change it to "Spend a lamp token" instead of use a lamp token.
Seems Interesting, not much to say.
I think this card is essentially balanced, but I personally don't like it. It's more of an opinion, so I have no objection to it anymore.
Needs a "Reveal's their hand" clause. Seems a bit weak as it will usually just trash coppers, whiff, or occasionally a silver.
Hilariously weak. If you are going by fan cards, LFN's harbor would be a good comparison. It can give +3 coins as well as a scouting benefit. Gladiator can give +3 and it costs 2 less. Count can give a +3 with a penalty and has WAYYYYY more flexibility.
Both very similar cards. A simple $4 gainer that gains a card costing up to 3 in your hand seems good. Fun fact: Donald actually tested a similar car for cornucopia, see the secret history.