Mow lawn with walnuts, chestnuts, hazelnuts on it.

Hi there.
For the short version just skip to the end.
This is the long version...
I've just recently moved to Slovenia and have a 'green' area around the house of about 3000m2, comprising of vineyard, orchard, vegetable patch, lawn and some forest.
I raked up the leaves recently and there's quite a lot of chestnuts and their husks (brown and prickly), walnuts and hazelnuts amongst the leaf pile.
It's a huge pile and I don't want to burn it. I would prefer to mulch it but I assume the nuts and shells mean this is not an option?
I am planning to build a dedicated leaf compost but if anyone has any other suggestions, I would love to hear them.

My other, more pressing problem, is cutting the grass and what type of lawnmower to buy.
I would prefer a push reel mower because of the lack of noise, it's good exercise, and a lot of the land is very sloped so I think a lightweight mower would be easier to control.
The downside is that a lot of the land is uneven...even the lawn is not completely flat with lots of bumps and mounds around.
But again, the big issue is the nuts and shells on the ground. I don't want them to damage the mower or blades. It would be too time consuming to clear them by hand.

So, the dilemma:
1) What to do with a HUGE leaf pile containing hard nuts and shells? Is composting the way to go?
2) What mower should I buy, again considering the nuts/shells on the ground?

Any advice or suggestions is most welcome!