Gear:
If you cannot do pve you're gonna have a rough time with gearing. Pve sets/accessories on sorc are VERY strong (sent, bloodlord, onslaught mainly - the other pve sets are not very good). You really should try to do at least 2-4 BS runs for the staff and bloodlord set since the staff is very powerful/ BiS for sorc and the set will save you ~4000 war crests vs buying full invader or full triumphant which are potential crest waste. Also need to do 4 BB runs for the sentinel ring so you can use sentinel talismans especially considering how weak your jewelry is currently.
4 BB and 4 BS runs is on average 8-12 hours of pve vs 100-150+ hours of crest grinding depending on efficiency, so skipping the vanquisher and invader ward is extremely valuable. You're saving ~5000 crests if you skip both.
You can go with Vanq after where you're at now if you don't want to do BB. Vanq is a good set too. If you can manage to do LotD the cape/jewel combo is also very powerful for sorc. After sent/vanq ward is done buy triumphant belt/boots and finish the invader ward with bloodlord or try to get it out of fortress bags I guess but that seems unreliable. Buy it only as a last resort.
After that I recommend buying main sov helm, shoulders, chest, gloves and jewel. You then mix those 5 pieces with your 2 pieces of triumphant that you purchased earlier and with LotD cape/jewel for 5/2/2 mix which will serve as your endgame pre-bis before triumphant ring where you would buy sov cloak and triumphant gloves and go 5sov/4tri.
If you cannot manage LotD, I suggest you can go with sov helm, shoulders, cloak, chest, jewel and triumphant gloves, belt, boots while holding on to the sentinel ring until triumphant ring. This 5/3 will be a lot weaker than 5/2/2 however.
Builds:
ST build gloomburst - for Scenarios and Kite/Roaming Parties. Gloomburst variant is more greedy and increases your own burst and damage dealt.
ST build proc - for Scenarios and Kite/Roaming Parties. Proc version is less greedy and increases your party members damage. Can be better damage than gloomburst build if you have active tanks and a good dps partner who are maintaining high uptime on target and activating their procs more.
Melee bomber build - Melee range wb aoe build. Can swap piercing shadows to neverending agony to make it more of a distance based build if you cannot get a guard or are in a pug warband where melee build is harder to play (usually know as Wave or Mid-range build)
ST/Aoe Hybrid - for Kite/Roaming Parties where you want to surf on warbands and need aoe pressure to secure more kill credit while still having the ability to deal high priority ST damage. Usually would only use this one during primetime when it's blobby.
Pve build - Looks funny because it kind of is. All you do is stand in melee range and spam Doombolt for bosses. That's the most optimal pve rotation. Disastrous Cascade/Shattered Shadows when aoe is required (but don't do it if your tank is skipping mobs, you'll just get aggro).
There's some other build variants like tap bomber but maybe too niche to explain for these purposes. These 4 should suit you fine for 99% of gameplay.
Rotation:
Rotations in pvp are almost always going to be situationally dependent but I can give some brief outlines. ST Sorc is all about "timestamping". This is a term used to describe when you are applying multiple damage instances within a 1-2 gcd time frame, thus stacking them for massive amounts of burst damage. Sorc is especially good at this and getting these combos down is crucial to proper gameplay. Keep in mind these are just guidelines (especially on aoe builds) and perfect rotation is not always possible and rotations change based on circumstance.
ST builds:
(Build to 80-100 Resource by spamming Ice Spikes/Infernal Wave out of combat before a fight)
Chillwind -> Vision of Torment -> Word of Pain -> Arctic Blast -> Gloomburst -> Impending Doom -> Hand of Ruin -> Infernal Wave
By doing this, you are ensuring that your Vision + Arctic Blast hit at the same time as well as your Word of Pain and Gloomburst shortly after then following with high damage instant casts to secure kills. You can also do baby rotation if the target doesn't die and you want to keep pressuring them or doing a "fake rotation" by doing the same thing but taking out Word of Pain (and optionally changing out Arctic Blast for Doombolt to make the timestamp a bit neater/harder hitting). Many players only track and look for Word of Pain, so doing a baby rotation with just Vision can catch them off guard and grant you extra pressure.
Melee bomber:
(Build to 100 Resource by spamming Ice Spikes/Infernal Wave out of combat before a fight or Impending Doom at range)
Ice Spikes -> Disastrous Cascade -> Surging Pain x2 -> Ice Spikes -> Impending Doom low hp target -> Infernal Wave -> Disastrous Cascade if still in melee, otherwise Shadow Knives -> Repeat
3.2 - Doombolt sometimes, mostly in pve or for ST rotation in place of Arctic Blast if you can reliably stand still for 3 seconds.
3.3 - Not really, unless you need to dump your career resource for some reason (which you should never do).
3.4 - Only in pve with close quarters tactic
3.5 - If you only have 1 target and can guarantee you will only have 1 target, sure. Otherwise you lose damage after that 1 target is gone.
3.6 - Refrain from using them unless absolutely needed. Handing out immunities is typically very bad. Never use aoe root randomly while in warband vs warband combat. Rooting will make your tanks unable to punt/aoe root and typically they want to do it not a sorc. In coordinated environments, aoe silence on the enemy healer line or a single enemy healer in an SC is potentially extremely powerful. Rooting/disarming/silencing in a 1v1 is fine at your own discretion.
Gameplay:
What you say is fine yes, focus unguarded always if possible. Never hit tanks in orvr, SnB tanks will block/disrupt everything. 2h tanks in SCs can be a target sometimes. Healers are iffy, with avoidance change they all have a lot more disrupt than before since they cannot be reduced below 50% by your reduced chance to be disrupted stat. In keep/fort you kind of just spam the choke with pit/wave/spikes etc while trying not to die, in pug situations aoe sorc is not fantastic for defending or attacking outside of walking in under tank m4 and doing aoe as normal.
Hope it helps.