Learn English – The plane arrives/will arrive at 3:30

1.) use arrive instead of arrives "When I arrive home, I will call my mom"

2.) arrived is past tense so it should be "When I arrive home, I will call my mom" or "When I arrived home, I called my mom"

3.) I think it's fine grammatically, but the phrase "on the heals of" seems awkward in this sentence

4.) This one is fine

I think #1 (corrected to "When I arrive home, I will call my mom") is the best, but #4 is good too.

Your approach is about probability of an event in the future but for this case, custom rules govern.

"am going to" is better to describe an immediate action, for example, the falling is going to happen in few seconds.

"Am falling" or "am about to fall" is also fine, serving a function similar to "am going to".

"Will fall" seems to lead people think that the falling is not going to happen soon, or only conditionally happens. For example,

"Help prepare my funeral tonight. I will fall at 10pm sharp." (Not going to happen soon.)

"Help reduce the weight or the plane will fall in an hour." (Conditionally happen)