If I respec skills with a skill at level 4 ready to be morphed will I keep the progress

This has been explained in one issue of their Ask us Anything series.

Do attributes (health, magicka, and stamina) affect more than just HP and your magicka or stamina pool (like resistances, speed, etc.)?

Yes. Your attributes will affect certain other stats. Some of these will be exposed, but others will be more behind the scenes. As an example, magicka affects not just how many spells you can cast, but their overall efficacy as well.

Quick rule of thumb:

• If your skill consumes magicka, then magicka will increase its number values.
• If your skill consumes stamina, then stamina will increase its number values.

Also note that - as this kb article explains - most weapon abilities will consume stamina, staffs being the exception as they consume magicka.

Do bows require stamina to shoot? And do Restoration or Destruction staves cost Magicka to use? Or is there some other resource used for staves?

Normal attacks with weapons don't require stamina or magicka. If players learn abilities for that weapon, these abilities will have a cost associated with them. Almost all weapon abilities, including those for the bow, will consume stamina. Staves are the exception—their abilities consume magicka.

See if I can answer all of your questions.

What exactly is the point of leveling a skill?

To gain access to higher level skills.

I sure do get that you can unlock new Skills and perks but does It do something else?

No.

Will you gain more Armor/Damage if you have a Higher rank in a certain skill in ESO or is it solely for the sake of unlocking new stuff

Yes. Not sure how much it scales.

Also if you Level up an Active Ability, will this ability get stronger or is it also just for upgrading an ability. If it's only for upgrading, then why can I further level the upgraded skill (I've noticed that you can upgrade an Ability only once.

Yes. Not sure how it scales though. I believe they are planning on implementing one more morph to the skill lines in the distant future.

Another thing I'd like to know is: What is the max level of an Ability/Skill

Rank IV > Morph Rank IV. Max Level of weapon/armor/class skills is 50.