Can characters block while fighting hand-to-hand or is my monk doomed to having an unused skill among his minors? Maybe I should go with a custom class, replacing Block with something more useful to him, if that's the case, while I'm still in the planning stage...

I just don't see monks fighting with shields and one-handed weapons...

No, you can't block while fighting with your fists. It is going to be a mostly unused skill, but the same counts for Blunt Weapons. It's not reallythat much of a bad thing though. You might level up a little slower than if you were using all your class skills, but that's actually good because the base game was only really designed for charaters up to level 20 while most characters would be well past level 70 by the time they max out all their major and minor skills.

Thank you for your answer.

My monk will use staves, so Blunt Weapon will increase eventually. And besides, weren't the expansions designed for higher level characters? Still, I suppose one unused skill isn't that bad, really. I had to learn countless skills during my education that I'm never going to use...

Tribunal is designed for levels 20+ and Bloodmoon is deisgned for levels 40+. You will still be able to get beyond level 60 even if you never increase Block.

The Monk class by itself allows you to reach level 76 by the time you max out all skills. If all your racial bonuses apply to class skills and you leave Block at 15 that's 85+45=130 skill increases less so you'd be able to reach at least level 63.

If you use a staff, a 2-handed weapon, you won't be able to block with a shield either. You can equip a shield with a double-handed weapon and get the armor bonus, you just won't be blocking any attacks with it.

Excellent. The character is a Khajiit, so yes, he will reach slightly less than 76, but indeed well over 40. This will be one hell of a test for my OCD-ish tendencies.