Much of the original "aural" tradition of these ornaments has been lost during the centuries when nobody had any interest in this part of music history, and there are few if any written instructions.
Note 1: there are contemporary written tutorials for later "early music" - e.g. the era of Purcell - but beware that ten different texts will probably contain more than ten different contradictory instructions regarding the same ornament!
Note 2: If you really need an authority to justify what you are doing, try something like Donington's "The interpretation of early music" - on line at https://archive.org/details/interpretationof010975mbp. But learning to make up your own mind about the issues is more fun than trying to slavishly follow someone else's opinions, however well-respected they may be. I expect most 16th century musicians learned how to play these ornaments just by listening, not by reading textbooks!
One line of attack is to compare different versions of the same piece in different collections, including lute tablature as well as keyboard versions of the music. Sometimes ornaments (particularly long trills) are written out in full in one source and marked with a sign in another.
In general the "tremolo" sign is some sort of trill, either long (usually in 16th notes) or short like a baroque pralltriller or mordent. There doesn't seem to be a definite convention as to whether ornaments start on the main or the auxiliary note.
"Harmony" isn't a very reliable guide here, since modern ears are so accustomed to common-practice harmony from the 18th century or later that some of the characteristics of 16th century music don't sound "natural" until one gets used to them.
For example 16th century composers had no concern about "false relations" like the G# and G natural in your second bar. Think of the music as basically contrapuntal, and imagine what you would do if the only notation you could see was your own monophonic part, with no knowledge of what anyone else might be playing. (This isn't so hair-raising as it might seem - jazz musicians do it all the time, often with no notation at all!) If one part contains an ascending "melodic minor" scale of A minor, E F# G# A, and another part simultaneously has a descending scale of A G natural F natural E, go right ahead and play it that way.
For example, you might prefer (once you develop an "ear" for this sort of thing) to play the second F# in bar 3 as an F natural. Others might disagree with you, but there is very rarely any "proof" as to what is right or wrong in such situations.
To compound the general confusion, the notation of accidentals in keyboard music was often somewhere on a scale between chaotic, confusing, or just plain wrong. For example, sometimes "cautionary" accidentals seem to have been added to the note before the one affected by the accidental, as a sort of warning - i.e. an F with a # sign actually means "this is F natural but the next F is a sharp"! Lute tablature of a piece is a great help in sorting out such things, since the tab unambiguously shows the actual pitches to be played. But remember that tabs written or copied by "non-professionals" in 1558 might contain as many mistakes in as similar tabs made by "some guy on the internet" in 2018!
If you were hoping for a nice simple set of instructions, this answer might seem hopelessly discouraging - but don't give up. Listen to lots of performances of music of the period, and then follow your ears. Your ears may be more reliable than editions like the one you showed - when that was made (around 1900) nobody except antiquarians were playing this music, and even if it was played, there were no audiences listening to it, and no recordings. Take the notation in such scores with a very large pinch of salt!
As for tempos, that is an easier question. Most of the music of this period was based on dances, or songs. The dances are well researched, and actually dancing them gives a good indication of the tempo. YouTube is your friend here.
Incidentally, this piece isn't "a Parthenia." (It's a Galliard, a common dance form, often following a Pavan - i.e. a quick dance following a slow one). The original edition of this collection of pieces was one of the first printed musical scores ever produced, and the full title is "Parthenia, or the Maidenhead of the first music that ever was printed for the virginals." The 16th century didn't have any hang-ups about sex jokes (Maidenhead - Virginals - say no more, nudge, wink!) or bad puns: another collection of similar pieces arranged for viols rather than keyboards was entitled "Parthenia inviolata" (groan...)
Final warning: in classical mythology, Parthenope was one of the Sirens, whose music usually ended badly for those who heard it!
