Where did the portal key go

There is no way to destroy own faction link, field or resonator (yet).

You can let the resonators decay, this will only takes 9 days if nobody recharges or attacks the portal and it will destroy all existing links.

XM charge, portal level and nearby targets will determine whether to try hacking a portal before taking it down. Is it a high level portal that will zap you for lots of XM, and you might run out of XM before destroying it or have other targets to attend to? In this case, don't hack while unfriendly.

Otherwise, esp. for portals that need a lot of repositioning and you will take almost 5 mins to kill them, always hack before attacking. Followed by another hack after all deployments are done. Never hack when its neutral or has just 1 resonator, unless you're fond of L1 items ;)

Why would you claim all portals before hacking one? You get 4 hacks, one every 5 mins. It is better to work on burning out portals you captured earlier while you attack remaining targets, unless you plan to do 20+ mins of hacking at the end.

When initially claiming a portal, are there any strategies to have a better chance of walking away with keys when you're done?

See Is there a way to increase the odds of getting a portal key?

In the case of acquiring portals, remember that attacking a higher level portal before you capture it might give higher level items, but overall less chance of any items. Thus, I expect that for keys its better to hack after it is captured, if you have to choose between the two.