It's everyone's job

Long story short, being entertained at a table is a shared responsibility. GM should welcome all players and create opportunities for the entire group and it's also up to the players to take advantage of these opportunities. Making an interesting character helps. Having your players create characters that fit the story helps even more. Doing the character creation together is strongly encouraged in many games. Not just the characters contribute to an interesting game. In play the GM should give player's many opportunities to do something engaging, develop their characters and have fun. It's up to the players to take those opportunities and use them further.

While you are not required to have a backstory, it is very useful to the GM. I've often used the rule of 6: every player needs at least 6 sentences of backstory, 6 paragraphs are recommended, but 6 pages is too long. I would recommend that you have some backstory that the GM can use, it's good for your own roleplaying as well. GM should accommodate for everyone present at the table, though, regardless of their backstory status. However, in your case the backstory problem is secondary to other underlying issues.

If one player gets much more attention thanhis peers, the group has a problem

It is true that some characters are easier to "hook" than others, but little backstory should never be used as an excuse to ignore one player. The fault is never equally on one side of the table, but what you said points to a case of GM favouring one player above others and taking over the play. As you said, that player made his character with the GM (while others I assume did not have that opportunity), is being given extra time and attention and gets to do much more than the rest has opportunity to.

This question has some excellent answers on how to deal with such a situation.

I suggest you leave the group at this point.

There is little that can be done to fix it if your GM is unwilling to listen and cooperate. To make the case clear:

1. A GM that rages because you have a shitty character is a shitty GM. A good GM would help you create a better character if that is indeed the case.

2. A GM that railroads and prevents players from branching out does not understand player agency. GMing is not playing with dolls. A good GM recognises that the most important feature for a player is freedom of choice.

3. A GM that is deaf to his player's feedback is doomed to fail. A good GM understands the symbiosis between himself and the players and listens to players carefully.

4. Actually, any person that asks for critique and then rages is hardly worth having around. It's fishing for compliments, not actual discussion.

You GM is not beyond redemption, but he will have to rethink the way he runs the game very carefully.

You may want to try and help him become a decent GM. I personally wouldn't. If you still would like to play with this group, you can offer to GM yourself or if the GM wants to listen point him to some good GMing for Beginners tips. You can also point him to this page.

Regarding round length

Note that sometimes a group has a Party Face, a character that acts as the main speaker and communicates party's intention to the NPCs. Many groups take turns doing the talking, but some prefer to have one character be the go-to talker. If you're uncomfortable with it, you need to communicate to the other players. In either case, turns should be shared, meaning that anyone can speak if they are a part of the discussion.

However, in combat, the turns should be as long as appropriate - there is no prescribed time that you need to fit to your turn. It's sometimes necessary for some turns to be longer (a cleric performing a complex multi-attack routine while activating magic items and casting quickened spells) and some shorter (I hit him with my sword!). However, in the long run everyone should get the same amount of **spotlight* and feel contributing and appreciated. That means that while the cleric takes more time describing what he does, the GM would devote more attention to the fighter, describing the effects of his actions in detail.

Your Reasoning is Correct...

... from a Rules as Written perspective:

Forcecage reads:

A prison in the shape of a cage can be up to 20 ft. on a side ... A prison in the shape of a box can be up to 10 ft. on a side ... Any creature that is completely inside the cage's area is trapped. [Emphasis mine]

The note on space (pg. 191) reads:

A creature's space is the area it effectively controls in combat, not an expression of its physical size. A typical medium creature isn't 5 feet wide. [Emphasis mine]

Therefore, since forcecage only describes the creature physically being inside the cage, and space does not represent physical size, a creature is trapped by forcecage if its body is fully within the cage, regardless of whether some of its space is outside.

To take your example (comment), a Storm Giant (MM pg. 153) is 26 ft. tall. It therefore cannot fit into a forcecage and therefore cannot be (fully) affected by the spell, regardless of whether or not its space is fully inside the cage. If the giant were to sit, or bend over, so as to reduce its height to under 20 ft., then it could fit inside, and could be trapped.

Physical size is everything, not controlled space.

Dragons

For this part of the answer, I am assuming that the measurements in the 3.5e Draconomicon apply to 5e.

The colour of the dragon is irrelevant in determining its size. The Draconomicon provides only a table of actual sizes by given size (tiny, small, medium, &c.). Although the table itself is huge (pg. 37), giving values for neck length, tail length, minimum wingspan, &c., I provide some of the more important values:

\begin{array}{c|ccc} \text{Size} & \text{Body length} & \text{Body width} & \text{Standing height} \\ \hline \text{Large (Young)} & 9ft & 5ft & 7ft \\ \text{Huge (Adult)} & 16ft & 8ft & 12ft \\ \text{Gargantuan (Ancient)} & 24ft & 10ft & 16ft \end{array}

Note that all of the values here represent not the maximum possible dimensions (i.e. tail and head completely stretched out), but the likely dimensions during combat (i.e. tail and head in).

Thus we can see that only the gargantuan ancient dragons are unable to fit inside a forcecage. However, dragons are clever creatures, and may stretch themselves out if they recognise that forcecage is being cast on them.