I have 3 issues that i wanted your advice on them please.
1.
If I use a thermally fused MOV (the fuse gets open when temperature is too high), how can i know when the internal fuse in the MOV got open?
Feed the MOV from AC through a high value resistor so that you get max 1mA or 10mA current through it. Look for the typical V-I curve for an MOV on a scope; if the fuse is open you will just see an AC waveform on the scope.
". . .how can i conclude from it when the fuse gets open depending on temperature?"
The graph you show doesn't tell you.
Fuses [and coils and semiconductors] have an I squared T rating; if a 1A fuse opens in 3 sec at 2A, then its rating is 12 amps-squared-seconds. This formula applies for part of the "trip" or "clearing time" curve.
These are on the Web but are hard to find.
Of course, a 1A fuse holds 1.1A or so indefinitely so the curve doesn't apply at this end of the curve, and at enormous current the clearing time also deviates from the formula.
It's I squared because heating in a resistor is proportional to I squared, and the ultimate temp rise which melts the fusible link is proportional to time.
Fuses also have an "interrupting" current rating. A residential 120v/240v supply may have a short circuit current of at least 20,000A, so a 15A fuse for this application has to be able to safely interrupt 20,000A.