mmmm...did I get the romanization all right?
Yes, you did it all right.
お皿をお下げしてもよろしいですか
o-sara wo o-sageshite mo yoroshii desu ka?
I like this one above^^ do you think I could say something like "sore/kore wo sageshite ii desu ka?/ as well?? while politely pointing at that something with my finger?
No, sore/kore sounds a bit rude to use towards your customer.
You should say sochira/kochira insead.
Also you need to put "o" before sageru. (not "sageshite" but "o-sageshite".)
And use "yoroshii desuka" instead of "iidesuka", which is a bit too casual to go with "osagesuru" which is very polite.
食べ終わりましたか
tabe owarimashita ka? I did not get this../finished eating?/ ??
To be honest, 食べ終わりましたか is a bit too casual here.
To ask a customer if he finished eating,
お済ですか？O-sumi desu ka? (have you finished?)
お食事はお済ですか？ o-shokuji wa osumi desuka? (have you finished your meal?)
By the way, do you think I could you this also??
あなたはそれを終えましたか
anata wa sore wo oemashita ka?
No. In Japanese language we do not use pronoun unless it is necessary to make it clear or emphasize which/what you refer to.
It depends on the situation, but using あなた to address to a customer can sound rude.
If you know the customer's name, use it "(name) sama" to address.
If you do not, use "okyakusama" instead of "anata".
Also as far as it is clear to the customer what you're talking about, there's no need to use "sore".
お済ですか is simple and just fit in this situation.