Can progressive tense be used for the progress of developing habits?

Solution 1:

As has been told you in the comments, "2" is not correct; it would be if you'd used the past.

• I got used to getting up at 7:30 am. (correct)

Why is not the present correct? ( I get used to getting up at 7:30 am.)

This is not too easy to understand; when you use the present in that way the particular form of that present is called habitual present (CoGEL § 4.6 p. 179), a type of use of the simple present.

Examples from CoGEL § 4.6

• We go to Brussels every year.
• She makes her own dresses.
• Bill drinks heavily.

(CoGEL) when they are used with the simple present, dynamic verb meanings, like stative verb meanings, usually imply an inherently unrestricted time span. But in this case the verb refers to a whole sequence of events repeated over the period in question.

In the first instance, the people the author is talking about went to Brussels several times and will keep on repeating this action for an undetermined time to come. The same idea of repeated action is found in "She makes her own dresses.": She has made several dresses (presumably over the years) and she will go on repeating this action as long as she finds this activity satisfying.
In the context of the sentence "2", there is not the possibility of a repetition with the action of "getting used to sth"; it takes place over a certain period of time, once, and as soon as the getting used to is fully acquired it stops and is not repeated; repeating it would have no meaning.
However, it is not quite simple and changing the context can make the habitual present correct for the verbal form "ge used to"; for instance, the following sentence is correct.

• When I start a new design I get used to handling the various techniques needed by brushing up on the use I have made of them formerly.

_{CoGEL: A comprehensive grammar of the English language}