As I understand it, -ip is used as a an alternative to and with successive verbs having the same subject. But, can it also be used to with gerunds, and participles?

as a verb: ... gelip ... giddim.

as an noun or adjective:  ... gelip ... given …

as a adjective:  ... gelip ... gidiğim. .. 

Adjective:  Gelip gittiğim ev.  The house which I come and go to.

                 Beni gelip soran adam nerede? Where is the man who came and asked about me.

Noun:        Sevip saydıklarım beni aramaz oldu. People I love and respect don´t call me anymore.  

                Gelip gören kaçıyor.  People who come and see run away.

The main use of the ´ip´ suffix is to save repetition when using verbs where the subject and tense are the same in a sentence.

It can obviously be used as a verb, but not without a subsequent verb to indicate the tense and personal suffix, as it has no meaning in isolation.

It is also used in a formula for saying whether/if XXXX or not

for reported speech with certain questions about actions.

O bana "Hasan´la konuşacak mısın?" diye sordu

He asked me "Will you talk with Hasan?"

O bana Hasan´la konuşup konuşmayacağımı sordu.

He asked me whether I will talk with Hasan or not.

Eşim bana "Senin bugün işe gitmen gerekmiyor mu?" diye sordu.

My partner asked me "Isn´t it necessary for you to go to work today?"

Eşim bana benim bugün işe gitmem gerekip gerekmediğini sordu.

My partner asked me whether it is necessary or not for me to go to work today.

Thank you gokuyum and Henry for the very clear examples.

They show the ecomomy of the Turkish language in speaking.