Syndicate Missions

[Repiru]

Do I have to equip the sigil for the corresponding syndicate before doing their missions, or is it okay if for example I equip a Steel Meridian sigil and do a Cephalon Suda mission? Will that gain me standings for both Steel Meridian and Cephalon Suda and a negative? Since Red Veil is the ally of Steel Meridian and Red Veil is opposed to Cephalon Suda, what will happen?

[GhostRipperNL]

The missions for the syndicate give the standing regardless, wether you wear a sigil or not for that syndicate. The sigil gives standing for the corresponding syndicate as well. 

Let's say the syndicate mission gives you 1000 standing, and wearing the sigil gives you 100:

The mission would have as effect:                                 The sigil would give you: 

Suda: +1000                                                                  Steel meridian: + 100

Loka - 1000 (100% -rep)                                               Loka: -50 (50% - rep)

Red Veil - 500 (50% - rep)                                             Red Veil +50 (50% + rep)

So, Red Veil would gain a little from the sigil, but lose a lot due to the mission. Syndicate missions give more than the sigil so the standing of Red Veil would lower. And of course it would give you standing for both Suda and Steel Merdian. For all the effects check this page: http://warframe.wikia.com/wiki/Syndicates

[NinjaZeku]

What ^ said.

Just to add though, wearing a matching Sigil will apply the % indicated on the Sigil to the mission's Standing reward.

E.g. wearing the +15% Steel Sigil on a mission that rewards 1000 Steel Standing,
you'll get an extra 150 Steel Standing that'll not be deducted from your daily Standing cap.

It's not a huge deal (and IMO not worth bothering with all the time)
but if you're serious about maxing out your Standing gains and stuff, just an FYI.

[MystMan]

The matching sigil part also works on allied syndicate missions.  Wearing a 15% Steel Meridian sigil (Champion) on Red Veil's missions will also give the 15% mission reward bonus. Saves you the time of having to switch sigils.

Wearing a sigil on the other syndicates missions will have no effect on the mission standing reward (only on the actual enemies you kill and actions performed in the mission, if you have any daily standing left). You will receive the base standing reward shown in the mission menu.

At low rank, this bonus might not sound like much, but on rank 5 missions, the difference will add up quite nicely in the long run. Rank 5 defense missions give ~5000 standing. Wearing the right 15% sigil will instead give 5750.