If I stick to the same speed (e.g. do not mix say 9 speed and 10 speed), can I mix the brand of chain and missing link safely. For instance, can I use a Shimano missing link on a KMC chain, or should I only use KMC links on KMC chains and SRAM links on SRAM chains?
Shimano recommends their 9 &10 speed chains be reconnected utilizing the specific speed link pin, which inserted with a chain tool. In my experience, there has not been any issue, including noise, using KMC's "missing link" or SRAM's "power link." Note that SRAM's 10 speed link is termed "power lock" and is suggested for use "one time only" because of the tighter tolerances present in ten speed systems. In practice, these can be used multiple times, no problem, but I base this on reading others' assessments not my own experience. Shimano's11 speed system uses a connecting link. Typically bike shops I frequent have KMC, SRAM, and Wipperman (product is called "connex") connecting links to choose from. Prices are similar between brands within same speed categories. Connex are a bit more money it appears to me. At any rate, based on the selection, why not stay within same brand for chain and connecting link? Regarding Shimano, I use the replacement link pin but again, no problems have been noted by myself or others when a Shimano chain is joined with a connecting link from SRAM, KMC, or Wipperman.
I've used SRAM and KMC missing links on 9- and 10-speed Shimano chains for years.
Shimano missing link
Good luck finding those, though...
Almost certainly, but do your homework.
At 9-speed, Campagnolo and Wippermann chains are slightly wider than the SRAM. So, Wippermann quick link works with Campagnolo but SRAM does not. There are probably combinations with similar issues at 10 and 11 speeds.