Hoping I can help you...
As far as I know, I would say 'yes' in both cases.
• if a single Walker attacks you, you fight back, and can use various skills, including Close & Ranged Combat, so the Gear bonus for weapons would work there.
But you can also use others skills (and the Gear for those skills would apply too).
• if you are fighting a Swarm (multiple Walkers/zombies) it is like above, except the skills you can use are limited according to the threat level (but Gear bonus can apply)
2. When fighting swarm/horde do you add weapon dice to your close combat/firearms skill?
• attacking Walkers first, as in Clearing Out an area, Gear would apply as well...
re. Gear, the basic rule is: "Provided that the GM agrees that the item is useful in the situation, you get to add a positive modifier to your skill roll when using it."
(and: Gear bonus cannot stack: "you may only utilize the bonus from one piece of gear").
Please excuse incorrect terminology as not near rulebook.
We cannot excuse you not being near the rulebook--what if the zombie invasion happens? How will you know the rules to fight them?!
Playing in France, and online