Since you ask specifically about fiduciary duties ...
These exist in common law and are in addition to and complement any statutory or contractual duties.
First, real estate agents do owe a fiduciary duty to their clients. The linked article breaks them into six categories, even though the duty is a wholistic one it gives a reasonable framework to think about it:
Obedience: You must obey your client’s lawful instructions.
Loyalty: You must always act in your client’s best interests, even if it means forgoing your own interests.
Disclosure: You must disclose any material facts about the transaction, including your relationship to the other party.
Confidentiality: You must keep your client’s information confidential unless you have their permission to do otherwise.
Accounting: You must keep accurate records of all money and property involved in the transaction.
Reasonable Care: You must use reasonable care and skill when handling your client’s business.
Urging a buyer to offer a higher price, even though it is good for the agent, doesn't mean it's a breach of the fiduciary duty. If the objectively assessed reason (i.e. by the judge after the event) is that the advice was commercially sound and in the best interest of the buyer, then there is no breach of duty.
Failing to follow the client's instructions to make an offer is more likely to be a breach of this duty but it still depends on the circumstances. It's always best for the client to give clear instructions, preferably in writing, or the agent may genuinely confuse an instruction as a discussion. Even where there is clear instruction the agent still has to act in the best interests of the client. For example, if while taking the offer to the seller's agent they are informed "My client (the seller) has told me to reject all offers below the asking price and to no longer deal with that prospective buyer" then it would not be in the client's interest to make the offer.