1) As far as I can remember, "Solo" queue actually lets you queue up to a team of two. This may have changed. Unfortunately, Solo Queue is just that - you and some strangers - and if you want an easy strategy to climb the solo queue ladder, there isn't one. You're largely at the whim of the matchmaker, so the best you can hope for is to carry a team, perhaps by playing a ganking jungler such as Rammus, Shaco, or Nocturne.
The current metagame theory is that teams with a jungler > teams without, so by playing a strong jungler (assuming you aren't overestimating your skill) will give you the best odds, as an early game lead can be hard to overcome.
2) Queue dodging in a ranked game no longer reduces your ELO, but it does prevent you from queuing for ranked games for a substantial amount of time. If you want to raise your ELO, you need to play games, and you can't do that if you constantly queue dodge.
You list primarily tanky supports, who were hit the hardest with the removal of Heart of Gold. This leaves two other GP/10 items: Philosopher's Stone and Kage's Lucky Pick. I ignored Avarice Blade as I don't feel it compliments the support role.
A Philo stone can build into Shurelya's Reverie, Eleisa's Miracle, or Ohmwrecker. Shurelya's is still a great support item, and Eleisa's reduces the cooldowns of the summoner spells Heal, Clarity, and Clairvoyance. It can also free an inventory spot if purchased early enough! Ohmwrecker is outshined by both items, and I don't recommend buying it on a support.
Kage's Lucky Pick turns into Shard of True Ice, Twin Shadows, Morellonomicon, or Will of the Ancients. The first two are most viable on a support, and the Shard continues to provide GP/10.
So a lot of things affect whether GP/10 is still viable.
For a Philo Stone:
- Did you take Heal or Clairvoyance?
- Do you need extra sustain?
- Does your team need a Shurelya's? Is anyone else buying one?
For Kage's Lucky Pick:
- Does your champion benefit from extra AP?
- Do you need additional CC?
Another new item is the Sightstone. For an investment of 950 gold, you can place up to 2 wards at a time, with each ward lasting 3 minutes. The Sightstone holds 4 wards total and refills when you return to base. This breaks down to 50 gold/minute, and starts saving money after 19 minutes (assuming you immediately place wards when available). It also provides +180 health, making it a strong choice for tanky supports.
Previously, GP/10 items were essential to compensate for the cost of wards. This is largely mitigated with the usage of a Sightstone, freeing money for other items.
A Philosopher's Stone costs 700 gold and pays for itself in 23.33 minutes. Kage's Lucky Pick costs 765 and pays for itself in 25.5 minutes. These times are halved if you sell the item. Because it takes so long to make money from GP/10 items, it's best to buy them as early as possible.
Compare this to the gold granted from kills/assists. A champion who hasn't been killed is worth 300 gold, and 50% of that for an assist. The more times a champion is killed, the less money the kill rewards, with a minimum of 15 gold.
Since 2 GP/10 items provide 60 gold/minute, you have to get a 150 gold assist every 2.5 minutes for assists to equal GP/10 items. You can get an additional 5 GP/10 from Quints and masteries, resulting in 90 gold/minute and needing an assist every 1.66 minutes.
The new pick-pocket mastery offers an additional avenue to generate gold. Unfortunately, this isn't very viable on melee supports.
While supports are no longer required to get GP/10 items to support expensive ward-buying habits, these GP/10 items are still cost-efficient for longer games AND they upgrade into items that are very useful for most supports.
Ultimately, the decision to buy GP/10 items comes down to play-style and preferences. If you prefer to play aggressively and need extra stats to stay alive, skip GP items. If you're trying to maximize gold gained, GP/10 is still the better choice (unless you can get an assist every 1.6 minutes!).
tl;dr: GP/10 is still very viable, especially since those items build into new support-focused items. However, it's no longer a necessity since the Sightstone makes warding much cheaper.
Best Answer
No your MMR does not drop and it will also not decay from inactivity. Really the only things that affect your MMR are winning and losing. Up until last Season Queue Dodging was used to "troll" the League system by playing into a promotion and then winning one game while dodging the other one. With this trick players were able to reach Diamond MMR while being placed in a Bronze league.
Basically, if you dodge you will lose LP but you will gain slightly more LP next game.