33 Seasons should keep you occupied a bit. Sadly earlier parts of it don't exist even in the BBC archives anymore.
No, but there are fan "reconstructions" that exist for all of the missing episodes. Complete audios exist, and a number of photographs were taken during filming; these are combined into the reconstructions, along with the occasional surviving clip or two. They aren't always an easy watch, but for dedicated fans, they're the only way to experience these lost episodes.
There are also a couple that have been animated (and more coming).
I definitely recommend Doctor Who, Brandon, but it's going to take you a long, long time.