Can problems in bitcoin protocol ever changed or modified. (I do not mean bitcoin core or something).
Problems do not change. They remain... problems. Did you possibly mean if the protocol can somehow change? (And if yes, how)
Yes, it can change if we ever come into an agreement. By we, I mean the community. By the community, I mean the miners, the ones who run nodes, the ones who run SPV servers, the developers, you, me, every person in this forum. If someone proposes a change, we ought to adopt it if it makes the system more practical than before.
If some disagree with the change, they can continue supporting the version prior the change the rest of the community agrees as proper now. If this change isn't backwards compatible we say that a fork occurs where the chain is split in two separate chains. If most of the users decide that the new chain is the proper one, the miners will secure that one and essentially most of the people will abandon the old chain.
An example of a fork is Bitcoin Cash.
If yes where can those problems reported.
Problems in the source code can always be reported. The source code is in
github and you can contact with the developing team.