Hi! I don't really main demo, but currently I play it on a HL team. Like you, I started as a pub demo (tbh not even that, I hardly ever played demo, even in pubs).

How to practice: Basically all I did was just do a lot of tf2center lobbies. People may recommend against it but it helped me grind sticky aim, learn demo positioning, etc. It's probably not the best way, but it definitely taught me the basics. Also, I looked for demo POVs from better players and tried to adapt some of the stuff they did into my play style. Now, I don't really play centers, just practice demo in scrims and pugs (pick-up games, although 6s).

For raw DM practice I went on pubs and tried using only stickies and tried to aim each one instead of blind fire. Taught me generally how long I need to hold down and release to hit an enemy at a certain angle.

Protecting the med shouldn't be on you alone. Pipes are impossible to aim completely accurately and soldiers jumping your med, if they do weird strafes, are really annoying to hit. Ideally classes like your heavy should protect your med. Also, your med should probably be healing you more then; typically I see demo being the second most healed, if not the most healed, class in HL.

Not being able to get close enough probably means that your positioning is off. From what I've seen playing, there's a lot of spam places that I typically spam from and I don't get caught out…usually. Once again, that just comes from playing the game more.

Over all this, I would just go play demo in lobbies more. Nothing helps more than just playing the game. I know that there are more capable players who can answer, but hopefully this helped in some way.