That is called the past participle.
Verb forms can be learned this way as: present / past tense / past participle. They are the three forms around which all tenses are formed.
'Get' can be used as a normal verb, as you've done in 3. and 5.
In 5. you are using the present tense, 'get' for a simple present tense statement. That should be simple. The simple past tense is, "I got a glass of water".
In 3. you are using the present tense of a phrasal verb, "to get around". Again, straight forward.
For the other three, you are using "I am getting + <verb>" or "I will get + <verb>. In all cases where you use another verb after a form of 'get', you use the past participle (the 3rd form as you call it). It doesn't matter what tense 'get' is in. 'Get' is the verb that inflects for tense; and the following verb form is always the past participle.
I get married; I am getting married; I got married; I will get married; I would have got married.
I'm getting used to it; I got used to it; I will get used to it, etc.
I get it done; I got it done; I will get it done, I have been getting it done ...
In sentences like this, you can think of 'get' as an auxiliary/helping verb like 'have' which changes tense while the participle stays the same:
I have done, I had done, I will have done ...
So, using 'get',
i) If it's used as a normal main verb (no other verb form after it) or as part of a phrasal verb, you conjugate it as a main verb.
ii) If it's a helping verb, you also use the appropriate tense of 'get' (conjugate it like a main verb) and use the past participle of the following verb.
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