I've always had great luck visiting my reps, either at home or in DC. The rarely get visits from actual voters and they and their staff love getting someone who is not a lobbyist as a guest. If you do so, have an ask, and most importantly have a story about how you or someone close to you is affected by whatever you want changed. Every time I've got things to move in a positive direction, and never once was I asked to make donations.

You can absolutely make appointments to speak to your representatives (Senators included). You're more likely to get someone discussing an issue they're working on, or that one of their committees is working on, but they'll see you for anything.

You can ambush them in a hallway or at a fundraiser, and they'll talk to you, but you'll have just as much luck making an appointment.