how do you visualize a word when you write?

I don't, I just write.

So for the letter t, do you just keep track in your head to write the vertical curve first then remember the horizontal dash after?

It's not really something to remember, past like.. pre-school where they first teach you to write, it's just instinctual to write it that way

For longer words, do you sometimes forget these final touchups?

Can't say that I have :p

Also does signing a signature come natural for you, i.e. due to the non stop motion?

Most people I know have a signature that consist of multiple strokes, so it's not really any more non-stop than any other kind of writing.

And not just "t" and "i", if you do the same thing for letters from other languages like accents from other languages too, e.g. á, à, ü...etc. Then please share your thoughts too.

We don't write accents typically in my native language, but we do have some special characters (ą, č, ę, ė, į, š ų, ų, ž) for the diacritic marks that aren't attached you'd treat them the same as writing dots on i's and j's in terms of write order, for ą, ę, į, ų the final stroke or the letter is in place to write the diacritic in the same stroke