How the party is formed in FFI is irrelevant. The 'legends' noted that four warriors bearing crystals would appear and set things right. You control those warriors. FFI was, obviously, the first FF, and the game was much more battle intensive than story intensive. It's difficult to fully explain the Time Loop, since anything dealing with time is highly theoretical. The most common explanation, however, suggests that the Warriors ended the Loop when they defeated Chaos, and thus changed history in a way that Garland never went evil in the first place. Thus, the contributions of the Light Warriors were rendered as not actually having happened. You could go into all sorts of speculation about parallel universes and the like, but I really doubt that Square had anything that complicated in mind for the first FF. The Loop was just a plot device.

The villain in FFII is Emperor Palamecia (or Paramekia or Paramecia, etc., depending on the translation). I'm not sure why you asked this, since you use the name in a rough form later in the post. The characters' reactions to the deaths of Josef and Cid are noted in the game (even if they're a bit wooden; remember that FFII was early in the series), as were their reactions to the deaths of several other characters.

Yes, Laguna really is Squall's father. They never state it explicitly, but there are so many contextual clues that there's no question that's the case.

If you had trouble with the Time Loop, I'm surprised you find Time Compression so lucid. Again, anything dealing with time can be interpreted many different ways. Admittedly, it's much simpler if you discount R=U, but it's still more complex than the 2000 year loop.

What goes on in Ultros' mind? Well, he's there solely for comic relief, so I'm guessing it's something like "Ha ha ha! I'm really funny! Ha ha ha!"

It's a shame you find FFVII's story too complex to enjoy. That story has always been my favorite. As to Cloud, a number of factors (Jenova cell injection, shame over his own weakneses, etc.) led him to confuse his past, often mixing his own memories with the experiences of Zack. This allowed Sephiroth to control him to a degree. To explain this fully would take a lot of space. I suggest you consult a plot analysis of the game. As to Sephiroth, much of what he was thinking is a subject for debate, although many facts have been established.

Guess that's all for now.