You did great.  This week will really stretch our healers in Kitten Brigade.  If we need you and you're able to step up, it will be time to bring you in.

Some notes about those parses:

1) Prim is specced and Glyphed into an interesting HT build, so his casts will differ greatly from my own, but he makes it work.

2) For trash, I generally regrowth+rejuve all the tanks, then WG the raid whether or not they have taken damage already. Heavy on mana, but thats why we bring mages =). Since the LB changes, I generally don't use rolling lifeblooms to tank heal anymore.

3)Consider the order you cast your spells. If you're going to hot up a tank with regrowth and rejuve, always cast regrowth first instead of rejuve. When you cast regrowth first, the GCD will already be up by the time the spell is finished casting, allowing you to get off a rejuve instantly, where if you cast rejuve first, you have to wait the 1.5s for the GCD to come around, THEN start casting your 2.5s regrowth. The difference is getting 2 heals landed in 2.5s, or getting 2 heals landed in 4s. Doing it with regrowth first allows you to get in an extra swiftmend, or even cast a full on Nourish, in the same amount of time. This is in addition to possibly getting a HoT tick,  allowing you to push more HPS, which is why people bring you to raids in the first place. =)

4) For the fights mori linked, the Vezax fight, while still being among the top healing, isn't something you should read into. Having no mana regen greatly changed how I heal. Mimiron, however, is a great example of having to use virtually everything in my arsenal. WG G5 during the heatwave phase, Nourish spamming the tanks in other phases, etc.

5) If you're going to nourish spam, make sure you start out with a regrowth as your first cast (unless the heal really needs to land that .5 sec sooner). Nourish gains a bonus to the amount healed for having a hot on the target, and since regrowth is your longest lasting hot, its the most mana efficient way to increase your healing. Also, since you have that hot ticking, you could also be spamming switftmend (for me, nourish might average 5k, but swiftmend will average 8k). Try and have swiftmend on cd as much as you can, its something I still need to work on.

There are some fights where rejuve spamming is godly. Especially fights where the raid takes constant, sustained damage, like Saph in Naxx. Other fights like Maly require group heals, but don't need to be instant (WG works perfectly). Still other fights require heals to have landed yesterday (like mimiron), in which case Nourish (or HT if thats your thing) ais ideal. Its all about using the correct tools in the correct situations.

Whether it's turning off automatic updates or control+alt+deleting before a boss fight to kill things on the process tab that are consuming significant memory, your lag was a problem - especially on Thaddius. I was worried it was behavioral, so it's a bit of a relief to know it was just your system -- but there are fights where being slow will kill you. Thaddius, Heigan, Malygos all come to mind.

Letting your system affect your performance week-in, week-out is the same as playing like crap, since the result is the same. Fortunately yours is free and easy to fix (though if an auto-update made you lag that bad you might want to invest in more RAM anyway), so don't let it come up again.