Yes. Another way to say this is " he grabbed her by the arm." But what you were thinking of is something like"he put his arm around her."

Country Skiing

I need to learn some lexicon about cross-country-skiing. Please, correct the text about my ski walk (ride?) today.

I decided to go cross-country-skiing today. I took my skis and sticks poles down from off the top of the wardrobe, and went out to the nearest wood. Normally, I put a particular wax, depending on temperature,   on the bottoms of my skis, front and rear, then a different wax for a higher temperature in the center, under the ski boot.  depending on temperature long the ends of skis some ointment for the same temperature outside and an ointment for the higher temperature outside in the center of skis under shoe place. I didn't put any wax ointment today, because often normally when I do, the skis start sliding backward. Sometimes when I wax my skis, I find myself sliding backward a lot, so I did not apply any wax this today.  Nevertheless, I was sliding backward more than traveling forward and had to use my poles vigorously to make any forward progress.    push against the ground with my sticks.  So, my arms got much more of a workout than did my legs.  Therefore, my arms got trained more than legs.

The ski trails were, however, in fine condition.  They had been recently maintained with a mechanical grooming machine.  

The ski tracks (ski runs?) were fine. They have been mechanically   maintained by snow groomers.

I am going to sleep.

I am going to sleep. And I would like to think about past day. Today snow has fallen out very much. And it will be funny New Year. Happy New Year.

I am about to go to sleep, happily thinking of the past day.  Today, a lot of snow fell. The new year promises to be fun and funny. Happy New Year!  Lots of ways to go, but just my idea.

The man's physique looked like a spark plug, short and stocky. No idea what a bespoke suit is though.

A number of differences really. If you are surprised by something you might be either, but shocked is, I think, stronger. If you are shocked you might be horrified or disgusted. You could be stunned in a pleasant way. Mrs Trump is a stunning woman, for instance. Of course you can receive an electrical shock or be stunned by a blow. I'm stunned that you would ask such an interesting question but not shocked!

Monty Python and the Search for the Holy Grail.      Very funny!

A really interesting question! Both could be correct, depending on the situation. 1. Addressing a person: You are late (Harry). "You almost missed the bus" something that might have happened in the past but did not, so the past tense is used. 2. A narrative in the present tense: You might be talking about yourself or another person. You (yourself or another person) are late. You almost miss the bus, but are lucky and get to work on time.