I giave up my seat on the train to elderly people. I gave up my seat on the train to elderly people.

"Recently" (in the title) refers to the past, so the past tense is expected here.

However, I usually sleep on the train because I've been exhausted lately, so. As a result, I often miss them. However, I usually sleep on the train because I've been exhausted lately. As a result, I often miss them.

I've been thinking lately that we first need peace of mind firstly in order to have athe kindness for other people. I've been thinking lately that we first need peace of mind in order to have the kindness for other people.

(1) "First" is more appropriate here; "firstly" is generally used to introduce a point you want to make. Also, "we need peace of mind first" is okay, but I think it's more natural-sounding to shift "first" in front. (2) "The kindness" might be more natural than "a kindness" here, because you're referring to a specific "kindness"—that for other people. (3) Instead of "other people", you can also use "others". I might prefer "others" here, because you'd already ended your first sentence on "people" not too long ago.

I've been thinking lately that we need peace of mind firstly in order to have a kindness forbe kind to other people. I've been thinking lately that we need peace of mind firstly in order to be kind to other people.