2 is not a beech but we need a closer view of the foliage to name it. Also a geographical location.

4 is a cherry.

Thank you! I'll try to upload a new picture of #2. We're in Maryland. #4 is just a cherry tree?

Arborvitae

Maybe another cherry

Witch hazel

Cherry

Cherry

Again - if you are talking about pollen allergies - cutting down/grubbing out half your yard isn't going to save her from all the other plants everywhere else she might react to. Including right next door.

One of the pollens I'm allergic to is that of poplar. This blows around on the air at flowering time.

Pollen can travel many miles. Here's a quote from an allergy site.

4. How far can pollen travel?

The answer will surprise you. In 1998, one of Levetin’s colleagues
1,050 miles northeast in Ontario, Canada detected cedar pollen from
Oklahoma in the middle of January. It took about a day and a half to get
there.

Weber points to a case where researchers found pollen on the remote
south Atlantic island of Tristan da Cunha – at least 2,800 miles from
where it naturally grows in South America.

More commonly, you should expect to be exposed to pollen from several blocks away, from trees lining civic boulevards to your local schoolyard.

Here is the site in case you want to read more:

https://www.allergicliving.com/2015/04/16/10-biggest-pollen-allergy-questions/

1 - arborvitae - possibly Green Giant, although lacking the pyramidal shape; could also be leyland cypress?

3 - wow didn't think of that, but that very well could be a witch hazel as was suggested

Thank you, all! I do see your point, Embothrium, and carol23_gw. I didn't even think about pollen travelling so far but it makes perfect sense. She does love her walks so I guess we'll have to limit during high pollen days. I just printed the article, Carol, so thank you for that! She's gonna have so much fun if she grows up continuing to appreciate nature (Claritin in hand, haha!)

In the meantime, here are hopefully better pictures of the "NOT BEECH TREE."