That depends on numerous factors, including: route, time of day, day of week, train-type, etc, etc. If you want an IC/EC train at an off-peak time, mid-week, on a less popular route, then probably yes. If you want an ICE at a peak time on a Friday on a popular route, then maybe not...

However, as far as I know, the DB ticket machines offer the same selection of tickets as bahn.de. So, even if you want to buy your ticket from a machine, you could look online for an equivalent day/time roughly one week from now, and see what's available. This doesn't guarantee there'll be the same availability when you want to travel of course, but it gives some idea. However, if you want to be sure of getting a good deal, the best advice is probably to book online, as early as possible.

Strangely, I can't find this specifically addressed on bahn.de anywhere, although it must be a common question and event. However, as long as the journey is all on one ticket, if a delay/cancellation of one train means you miss another, you can then take the next available train to reach your destination. It is wise (although I'm not sure if it's absolutely obligatory) to get the conductor on the delayed train (or staff at the station) to write on your ticket that the train was delayed, and that the 'zugbindung' (specific train) condition has been lifted. The Deutsche Bahn staff can also advise you on the best new connection to reach your destination. (I'm not sure to what extent you're allowed to re-route, or upgrade to a higher category of train, yourself - but if DB staff say you can, then presumably it's OK.)

I had a situation last year, where I missed an EC (on a zugbindung ticket), and was allowed to take an ICE as an alternative.

See also the discussion in this thread: Bahn.de - Missed Connection

If anyone can find a page on bahn.de that spells out this rule, I'd be interested to see it.