You need to recognize burst gankers like Tiny are a threat early in the game and adjust your play around them. Typically, this means that I'll be picking up strength Power Treads and/or a Bracer to give myself extra strength to survive. If the other team has multiple magic damage heroes, you can also look into picking up a Cloak or even a Hood or Pipe.
This should prevent Tiny (or Nerubian Assassin, or a few others when they're ported) from ganking you by himself, he'll need teammates or a truly massive advantage to do so. Tiny has powerful burst but after his combo (which deals ~900 magic damage, ~675 damage to standard magic resistance) plus the damage from a couple of autoattacks, if he hasn't killed you there's no way he should be able to: you have your own spells and hopefully aware teammates.
Other things you can do to prevent a Tiny from snowballing apply to every game: have good wards up at all times and help your middle lane rune control if possible. Limiting Tiny's early game mana really slows him down because he's not much of a threat without that 240 mana to combo. You can also put strong laners against him, since Tiny has such low base armor, and seriously limit his early game farm. Some common options to counter a solo melee hero in mid lane include:
- Ancient Apparition
- Batrider
- Viper
- Venomancer
- Warlock
- Lich
For a solo lane, you want a hero that's somewhat level dependent, as they'll be getting a lot of experience. This could be someone like an Invoker, Leshrac, or Night Stalker. If this lane is solo mid, ideally they'll also be able to utilize runes well to gank, because they'll have the easiest access to them.
As yx. sort of pointed out, it's much harder to gank through the opponent's jungle than through your own, making the "safe" or "short" lane the one alongside your own jungle. This is typically where a hard carry hero who needs a LOT of items like Anti-Mage or Faceless Void will lane. However, melee heroes in lane are subject to a lot of harass so they'll almost definitely be paired with one or two support heroes like a Dazzle or Crystal Maiden, who will earn a small bit of gold for themselves and maintain lane equilibrium by pulling neutral creeps.
Conversely, the "offlane" or "long" lane is often against multiple opponents and is easy to gank, so you'll want someone there who has a natural escape mechanism ability, like a Windrunner, Puck, Dark Seer, or Mirana, all of whom can be productive just with levels and not much gold, which is exactly what they're likely to be getting in a "suicide" solo lane.
A hard carry is a hero who in lategame with a decent amount of items will be able to deal large amounts of auto-attack damage quickly. They usually have abilities that will make an item on them stronger than the same item on another hero. For example: Gyrocoptor's Flak Cannon, Juggernaut's Critical Strike, and Weaver's Geminate Attack all grant extra damage. These heroes usually have large AGI growth per level or are AGI heroes, which allows them to gain high attack damage, attack speed, and armor from the same attribute.
Some hard carries are also increasingly powerful into the game because they are able to farm at far faster speeds than other carries can match. They have good base stats and/or good mobility and thus can hit a "lategame damage" stage faster than typical carries. Some examples include Anti-Mage, Shadowfiend, and Naga Siren. In addition, there are some unusual hard carry heroes like Spectre, Morphling, and Obsidian Destroyer are able to do so through unorthodox abiltiies. I wouldn't worry too much about that.
The terms aren't very uniform, but "soft carry" or "semi carry" usually refers to heroes that do better with items than the majority of heroes, but not as good as a hard carry. Examples of these might be Windrunner, Mirana, and Stormspirit. While they can potentially carry if they have a good enough early and midgame, with an equal amount of gold in items they are expected to be weaker than a hard carry. They make up for this by having a stronger laning phase/earlygame and having stronger abilities.
Finally, a term that's gaining more traction recently is "midgame carry" for heroes like Razor, Necrolyte, and Krobelus. These heroes deal a majority of damage from their abilities, not from their items, and so they peak in terms of effectiveness when these abilities are maxed, usually somewhere between levels 11 and 16. This is much earlier than a typical carry who just gets better and better as he gains levels. However, they are still fully capable of ending a game in this window of time if left unchecked.
Hope that helps. -.-
Best Answer
Since hard carry is, in my opinion, the easiest role to play, I would try to safe trilane with a random if I were you. By your MMR, I presume that you probably know how to safe trilane, but I'm going to lay it out briefly anyways for others' benefit.
First, it's not literally a "tri-lane." That is to say if you have three people in the lane from your team at once and you aren't currently ganking the enemy hero(es) into next year, you are not doing it correctly. The tri-lane usually involves a carry and a babysitter as is normal for pub play, but there is a second support that consistently pulls your creep wave into the jungle so that they die to neutral creep and deny the enemy XP and gold. You can do this with a duo lane too, but it's riskier for your carry because they get left alone for at least half the time, and you're alone too which means that if mid ganks through jungle you are also paste. The support in the jungle gains XP by consistently pulling creep from the neutrals dying. He or she can also leave to gank mid or do some general roaming stuff, if you think that it is safe to duo lane for the moment.
Second, in terms of lane comp, you should be focused on "what heroes work well ganking or teamfighting together," not "what hero is the best at sustaining lane presence or helping my carry sustain his presence in lane." Undying and Visage are famously good trilane heroes in almost any comp because they both have skills that benefit greatly from more combatants being in a fight at once, and they're powerful early. Other possibilities include specific comps that synergize well together. A good one might be Ursa + Witch Doctor + Crystal Maiden. CM can set up easily with Frostbite, then WD moves into position and uses Maledict. Once Frostbite expires, WD stuns. Meanwhile the whole time Ursa is laying into them with Overpower and Fury Swipes. If they aren't dead outright then Maledict is guarenteed to kill them because between CM and Ursa you have a very large amount of early game burst damage, which translates into Maledict having huge ticks. That's just one I thought of off the top of my head, just think about the spells of all the heroes you've played and how they might work well together.