Do I need to complete all of the "Radiant" quests that Aela the Huntress gives me in Skyrim???, please help.

No, you don't "have to" complete them all.

Can you be a little more specific though. Your question seems too broad.

You can't really complete all the Radiant quests. The game will just keep generating more... Hence, the "radiant quest system".

Do the quest that Aela the Huntress gives me to go to Greywater Grotto to kill the animals "Animal Extermination" quests need to be completed to get Aela the Huntress to become my companion and marry me in Skyrim???

Okay, thanks for the clarification.

To get married, no you don't have to do radiant quests. The first thing though, is you must complete the companions main quest. You'll know it when you finish it.
After that, you have to travel to Riften, go to the Bee and barb inn, and purchase an amulet of mara. Go back to Aela, then ask her to marry you.
Follow the directions, and you should have a new soulmate by sundown.

But, you do not have to finish all the "animal extermination" quests to do this. You MUST finish the companions main quest line though. If you are unsure if you have, ask Aela to follow you. If that option appears, you have finished the main quest. You will see the option to ask her to follow you after you finish the main questline. Once you see that option, follow the above steps and your good to go.

What quests are all of the Companions questline "MAIN" quests in Skyrim the PC version???, please help.

If you have the achievement "Glory of the Dead", you've finished the Companions main quest line.

Here's the main quest list.
http://uesp.net/wiki/Skyrim:Companions#Main_Quests