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For instance, can I simply trade the contract cost without ever having an obligation to the shares? For instance, let’s say I buy a call contract at $2.50 ($250.00) and the next day the stock rises and the same call contract is worth $2.55 ($255.00). Would I be able to sale the same call contact for the $2.55 with no other obligations even before the expiration? Does it also work that way with put options?
Thank you

<<<can I simply trade the contract cost without ever having an obligation to the shares?>>>

Yes. The only time you have an obligation is when you have written an option (sold an option you do not own).

<<< For instance, let’s say I buy a call contract at $2.50 ($250.00) and the next day the stock rises and the same call contract is worth $2.55 ($255.00). Would I be able to sale the same call contact for the $2.55 with no other obligations even before the expiration?>>>

Yes

<<<Does it also work that way with put options?>>>

Yes

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One important thing you need to understand is that the price of an option depends upon more than the price of the stock. It is perfectly possible to buy a call option but see the price of the call option go down even though the price of the stock went up. Similarly, it is perfectly possible to buy a put option but see the price of the put option go down even though the price of the stock went down.