1) Yes, you can.
The only exception are:
- Metamagic feats, you need the proper feat to craft each type of item.
- Spell Completion items, you need to know the spell to write a scroll.
- Spell Trigger, you need to know the spell contained in the wand or staff.
Everything else you can simply increase the DC by 5 points per requirement missing.
Using your example, the Ring of Gate has a normal DC of 27 (10 + item's caster level, 17), if you know the gate spell. If you don't know the spell, or if you cant pay for someone to cast it every day spent crafting it, then you must increase the DC to 32.
2) You don't have to provide all requirements by yourself, you can get help from others. Example: a cleric could craft a Wings of Flying with the help of a wizard. But everyone helping you must be present every day spent crafting the item, otherwise the process must be started again.
That said, yes you can make any item, even if you don't meet the requirements, the increased DC means you have to take different approaches, research a different ingredient to replace the missing spell and stuff like that.
3) No, the caster level is the default DC for every item, it is also used to roll saving throws for unattended magic items, and to define the spellcraft DC to identify them (15+CL).
To craft a Ring of Gate, all you need is enough spell ranks to beat the DC 32 check and have the Craft Wondrous Item feat.
Best Answer
No, the relevant rules can be found in the entry for Magic Item Creation in the Pathfinder SRD.
To briefly summarize, the caster level of the item is part of the DC that you need to roll against when you make a spellcraft roll. (nominally 5 + Caster level of the item).
It also set other characteristics of the magic item such as how difficult it is to dispel.
Creation of a magic item is controlled by several prerequisites all of which are listed in the construction requirement in the magic item description.
For example Ring of Protection requires you to have the Forge Ring Feat, know the Shield of Faith spell, and have a minimum caster level of three times the ring's bonus, and pay the costs from the attached table. Shield of Faith can only be cast by a cleric, oracles and/or inquisitors. Finally will need a spellcraft (or craft) roll of 10+ due to it's caster level of 5.
This also has been addressed on an official FAQ: