1.

I am not sure how to translate this into one sentence in English.

But I will explain it separately.

「我的第一志愿是」= My first wish is

「夹菜」= pick up some vegetables/meat/...
In a restaurant, you can use 菜 to refer to one any item on the menu.

「喂饭」= feed someone with rice

「盛汤」= make soup, which I mean the action you use a ladle to dish out some soup.

「擦嘴」= clean your lips

Actually the original sentence makes no sense to me.

It's like saying "My dream is to eat."

2. which is the difference between 理想 and 志愿

理想 is more colloquial.

Actually they are the same in many situations.

They both mean a practical purpose you want to achieve.

The only situation I know is we use 志愿 when there are more than two options.

And we use 「第一志愿」「第二志愿」to mean something like "First wish" and "Second wish", I don't know how to express them in English.