Are there any websites to check if my luggage will be accepted at airports?

A few things to note

1. It can be confusing: Every airline has their own set of rules and it can even vary with aircraft type and type of ticket
2. I don't think there is a single website that has all regulations in one spot. Check with the airlines you are trying to fly with. For example: here is what United has https://www.united.com/CMS/en-US/travel/Pages/BaggageCarry-On.aspx
3. It's not quite as complicated as they make it out to be. It typically works as follows
4. For checked bags (cargo hold) you have a baggage allowance which depends on your ticket. It spells out the number of suitcases and the maximum weight. There is also a size restriction but unless you have a really unusual piece of luggage, that's not a problem. If you exceed the weight or number, you need to pay extra. Typical example would be "1 suitcase of up to 23 kg".
5. On the plane: Most airlines allow you to bring one carry-on bag plus a personal item (back pack or purse) on the plane.
6. Carry on is restricted by size or weight (or both). A standard roller board (22 cm x 35 cm x 56 cm), will fit pretty much any regular aircraft. Weight limits do depend on the airline. Lufthansa, for example, limits to 8 kg https://www.lufthansa.com/us/en/Carry-on-baggage. United does not restrict weight.
7. If it's a very small aircraft that doesn't fit a normal carry, they "gate check" the bag: You give it to them when you board and you get it back right at the gate when you exit (not on the regular baggage claim).
8. Personal Item: That's typically a back pack or a purse. Usually, they are not picky about the size if it first under the seat in front of you. That's different if you have a "basic economy" or highly restricted ticket. In general, the cost savings aren't worth the bother, so I would avoid these
9. What goes where: If you check a bag, put all the liquids in there. If you don't, you have to make sure that you that all liquids are less than 100ml and fit into a quart (1 liter) sized bag. Keep laptops, notepads, phones with you in carry on. In fact, laptop batteries are not allowed in the cargo hold.
10. At security: Every airport has somewhat different rules, but typically you need to take out liquids (up to 100 ml each), laptops & tablets. Empty all your pockets. Take off coat, shoes and belt. All that stuff goes through an X-ray machine while you go through a metal scanner or body scanner. Once you are through, you can collect your stuff and repack everything. It's easy enough: just watch what everybody else is doing.