Exercise for English course

I just finished this exercise and I need you to help to me correct it. I must need to put the verbs in brackets in the correct com (no sé qué quieres decir con "com") and I must also give reasons for why.

Dear Jill,

I've just got back from climbing (after preposition) Mont Blanc in the Alps and I must tell you what a great time I had. On arriving (after preposition) in Chamonix we were introduced (past tense, after 'were') to our guides. We were then kitted(no tengo ni idea de qué es esta palabra jaja) out with ice-axes, crampons and climbing boots and were sent straight out into two days' training (after presposition) in and around the Le Tour glacier. The guides used this time to assess (after used this time) our ability to make (?) the ascent and to teach (?) us the basics of mountaineering (after preposition), such as how to use (after how) an ice-axe and how best to work to work best (after how) in a team.

The first day consisted of climbing (after preposition) for five hours from the Nid d'Aigle to the Gouter Hut. I thought I'd be too cold sleeping to sleep(?), but in fact that wasn't a problem at all¡

Day 2 started at 2 am with a four and half hour walk to the summit.

Reaching (the subject)the summit was only a third of the day's work. The descent route included jumping across gaps in the ice, and took seven hours.

I'm really looking forward to seeing (after look forward to) you next weekend so I can tell (after modal) you all the details.

Love, Sue