Is this interference...?

You're asking about obstruction, not interference. (The defense obstructs, the offense interferes.)

Pro rules, this is not obstruction. Pretty much anything else, this is obstruction.

It depends on the rule set. It also doesn't matter until the runner is actually hindered. So the mere fact that the fielder is standing between the runner and the base is nothing, until the runner heads back to the base and is hindered by the fielder being there.

In MLB, if the throw is on the way, and the runner is hindered because the fielder is in the way, this is NOT obstruction. It is a legal play.

For almost all other levels (NCAA, high school, youth ball) if the fielder does not have the ball and the runner is hindered, it is obstruction. (It isn't in Legion ball, and it might not be in some others.) There is an exception if the throw is such that the fielder had to move to that position in order to attempt to glove the ball. (A typical example of this is an off-line throw to 1B that pulls the first baseman into the path of the oncoming batter-runner.)

The penalty also varies by organization. In MLB, obstruction during a play on a runner results in a dead ball and a minimum one base award to the runner being played on. Same applies to most youth ball, because their rules are usually based on MLB rules. I think NCAA and high school use the same ruling, which is different from pro rules.

It would be a judgement call by the umpire. If in the eyes of the umpire that the 1st baseman got in the way of the runner because he did so while attempting to catch the ball then it's not interference. In that case, the runner must run or slide around the fielder. However, if the umpire judge that the 1st baseman deliberately got in the way of the runner for the intent of blocking his path to the base, then yes, it's interference.

Most umpires will only call obstruction if there is contact made. So if the BR tries to avoid and go around the F3 without the ball in hand, they won't call it. If the BR dives back to 1B and makes contact with F3 without the ball in hand, they will call obstruction.

This applies to everything except MLB.

it all depends on the umpire, and what he saw.