Thank you
pattiewhack for pointing out this post. I have been under the weather for a few weeks with breathing problems.
rawypetit - sorry it took so long to reply but here it goes.
1. 1795 Mo FM - this is a cast copy that looks as if it was used in jewelry with a top center mount. The details are too "soft" to be real.
2. 1813 Italian 5 Lira - this appears to be one of the series of Modern replicas of older 5 Lira coins. They are well made but use modern dies. What does the edge read? FERM is not on the originals but is found on the replica copies.
3. 1782 Mo FF - This is a cast copy made most likely in the 1950s or 60s for the tourist trade. There appears to be a trace of a top mount or a sprue at the top of the coin. In addition the rim stands up too high above the field.
4. 1791 Mo FM - this coin looks like it could be real. The weight is good and the details look pretty good. There does appear to be a repaired hole near the rim at the top of the coin - through the King's forehead. This may have been a jewelry piece for years accounting for the softening of the detail.
1813 Lima JP - this is the most difficult coin to be certain about. The coin was definitely mounted and wear could be from day-to-day use. The method of manufacture and remaining details look good to me - BUT the weight would clearly indicate a forgery. What would possibly account for that much metal loss when there is still some "detail left" ?

- I wonder - Has the edge been smoothed - filed - to remove the original engrailled edge design? Only that could account for the missing weight.
I hope this helps. If you have other questions please contact me directly when you post so that I won't miss the question.