Technically the Aerospray is considered the best weapon for straight-up inking, which is the main objective of Turf Wars, but the Jr. is right up there with it. It kills decently fast if you can get in close, which is admittedly difficult at times but not impossible. The short range is indeed its biggest weakness, so you want to avoid situations where opponents can find the space to out-range you (in other words, ambush people as much as possible; there are other reasons why this is a good idea in general, but that's going a bit off-topic). The Bubbler is still among the best specials in the game as well - invincibility is always useful, and even more so when you can pass it to teammates to bolster a push. It compliments the short-range nature of the Jr. well, giving you that extra edge in a close-quarters fight, and the Jr.'s high inking efficiency only helps you charge it up faster. Let's not forget the Splat Bombs either. I personally find them to be the most versatile of the three types of "grenades" - they're powerful enough that you have to respect them, much like Suction Bombs, but they also don't take forever to explode like Suction Bombs do, so you'll be able to get a lot more kills with them. Splat Bombs also benefit from the fact that they don't explode or stick in place immediately whenever they touch a surface, meaning you have more options for placing them in otherwise hard-to-reach spots, including around corners.
To follow up on some of the above posts from today, I'm not sure how much I really "depend" on Bubbler myself. I know I won't always have it available, and I try to put emphasis on generally mobile and evasive play first and foremost, so it's not something I think about that much. However, given how powerful it is, I say why shouldn't I be trying to get as many of these bad boys as possible?
I don't have a ton of experience in Splat Zones with the Jr. yet, and none at all in A-rank play, but the most I can say is that the Jr. is arguably best used as a supporting weapon. Longer-range weapons abound in Splat Zones, so you can't just freely travel everywhere either. What I try to do is focus on its strengths, namely, its ability to quickly ink areas, its relative mobility compared to some other weapons, and the Bubbler. I've seen plenty of A-rank players who use the Jr. from streams and such (never the streamers themselves though, just others in the lobby), so it's definitely possible.
Any Bubblers that you pass to teammates end at the exact same time yours does, so yes.