11.Where can I hire mercenaries?
Small numbers of Welsh bowmen, Flemish crossbowmen and desperate untrained peasants are readily available for hire. Mustering larger numbers or locating other types of troops will require significant travel.
12.Is there any place on the map where swords are illegal, magic is outlawed or any other notable hassles from Johnny Law?
The main issue is that spellcasting or being a spellcaster is not illegal, but Black Magic is a serious crime. Black Magic is defined as casting a spell intending to harm another.
13.Which way to the nearest tavern?
Bad news, my thirsty friend. There are no taverns in fake 12th century Cornwall. The only taverns in the setting are leftovers from the old Roman road houses and the Roman construction crews never got this far. But you can find alehouses fairly easily. These are simply peasant hovels where the wife and daughters brew extra ale. You can only visit them when weather is good, since all the seating consists of stools or benches set up in front of the place. But most peasant households brew their own ale, so flash a little gold and people will literally come a-running with a bucket of ale to sell you.
14.What monsters are terrorizing the countryside sufficiently that if I kill them I will become famous?
Bodmin Moor is said to be haunted by some sort of cat monster, possibly an undead cat monster or a cat monster from Hell. Reports vary.
Also, the last known dragon in 12th century pseudo-England (which does an even better job of keeping Cornwall oppressed than the Normans) lairs somewhere in the dungeons below Castle Dundagel, which is literally right next to the Caves of Myrrdin.
15.Are there any wars brewing I could go fight?
Besides the ongoing conflict between King Stephen and Empress Maude, lots of pettier conflicts are in the offing. Any land hex on the map could be in the middle of some level of warfare when visited.
16.How about gladiatorial arenas complete with hard-won glory and fabulous cash prizes?
Not that you know of. Gladiatorial contests are condemned by the Church as pagan and barbaric.
17.Are there any secret societies with sinister agendas I could join and/or fight?
Much of the sinister agenda stuff seems to be going on right out in the open in these wicked days. Satan has his own underground (often literally so) church. Imagine Anton LaVey as a pope made of anti-matter and you have the gist of it.
18.What is there to eat around here?
Since you're staying at a monastery, probably lots of porridge and coarse bread with a tiny bit of meat. Fish on Fridays if not more often than that. Once you have some ready cash poachers will no doubt sell you fresh-caught game at a mark-up.
19.Any legendary lost treasures I could be looking for?
Due to the semi-historical nature of the campaign you can probably think of some yourself: Excalibur, the spellbooks of Merlin and Morgan le Fay, the Shield of Hercules, the Ark of the Covenant, etc., etc.
20.Where is the nearest dragon or other monster with Type H treasure?
See question 14.