The AI uses a variety of internal factors to decide where to reinforce -- such as, it prefers to reinforce on home planets or planets that are adjacent to its home planets -- and it also does give a bit higher weight to planets next to planets where humans have a large presence. But there is also a huge random component to this, as well, which makes for interesting populations over time.
The general rule of thumb is, don't trip the Alert Level on AI home planets or the ones adjacent, unless you're ready to deal with those. If your fleet is substantial enough in the staging area next to the AI Home planet, that will trip the Alert Level (see the intel summary) regardless of what kind of ships the AI has on the planet you are at. It treats all neutral planets as hostile, so if you've completely kicked it off but have not taken the planet it doesn't matter (it assumes you might be using that as a staging point for a big fleet, whether you are or not), and when it still does have ships there, even a few, of course it can see your big fleet same as you could on its planets. Really, it treats any planet it doesn't control as hostile, and planets that it does control, but which you have a big fleet on, as hostile.
So, to answer your questions, you are indeed telegraphing your intent to the AI to some extent, even though it doesn't necessarily know you have a big fleet there. It just knows that its home planet has now been exposed, and so it will reinforce heavily there no matter what you do now. Previously, the better strategy would have been to build up your fleet on a planet two hops away from the AI home planet, and then send that fleet through hostile territory to take them unawares. Now you'll want to just go in and clip off as many of those guard posts of the AI home planet as possible, and that will reduce the ship cap overall. You'll then want a really big fleet in order to take out the actual command station and the mass of ships that is no doubt around that. That mass will cap out at some point, so it's better to wait until you are really ready and have a huge fleet, compared to trying to rush in and repeatedly whittle them down, because they'll outpace you (because of the way the AI reacts to fleets on its own planets, see below).
Pretending to threaten other planets won't help against their home planets, but it can help against other planets you want to take, to a small extent. The reason is that the AI will divert reinforcements to planets that have big fleets of human ships on them -- not nearby, since it doesn't generally know that they are nearby, but they can mobilize pretty quick when you are attacking, as you may have noticed. But, the home planets, when threatened, still take priority over even big fleets elsewhere, so you can't divert their attention in that fashion.
Good questions, let me know if you have any others!