Dale M's excellent answer covers a lot of your questions. I will try to answer a few things I think were neglected, especially focusing on the issues that may not be clear to you as a new player or with an inexperienced DM.
You've got to see something, but you also have agency
The party enters a new location, and the GM asks us to roll a d20 for Perception. We all roll, and the best score is 14. The GM then tells us that we do not see anything and that we can proceed.
Based on your description, it seems that your DM has a fundamental misunderstanding of how Perception is supposed to work, and indeed the underlying process of playing the game.
- The DM describes the environment.
- The players describe what they want to do.
- The DM narrates the results of the adventurers' actions.
The party enters a new location, and the GM asks us to roll a d20 for Perception: When your party enters a new location, your DM should not immediately be asking for a roll. Instead, they should be describing the environment to you, telling you everything that you can see without a roll, everything so obvious that a roll is not needed.
In addition, they should also be telling you things you can see with your Passive Perception (emphasis mine):
Passive Perception. When you hide, there's a chance someone will notice you even if they aren't searching. To determine whether such a creature notices you, the DM compares your Dexterity (Stealth) check with that creature's passive Wisdom (Perception) score, which equals 10 + the creature's Wisdom modifier, as well as any other bonuses or penalties.
So if you enter an area with a hidden rogue, a secret door, a subtle draft, etc, your DM should also be describing these things without a roll, provided at least one of your characters has a good enough Passive Perception to spot them.
Once the DM has finished telling you everything you notice without a roll, then the players describe what they want to do. At this point, you can either tell the DM that you want to move on or that you stop to search the area or investigate some feature.
It is only when you ask to do something that requires resolution that the DM narrates the results of the adventurers' actions. Even here, a roll may not be required. Simply the act of declaring your intent of interacting with the environment may reveal something. "I want to search the room," could tell you the names of the books on the shelves, that there is a piece of paper under the divan, or that a goblin is Hiding behind the curtains, all of which might be resolved without a roll, but none of which could have been seen without your declaration of your intent to search.
It is only when you ask to do something that requires resolution and for which there is both a chance of failure and a chance of success that the DM should ask for a roll (note that this is more advice than a rule).
In this case, a roll better than your Passive Perception (anyone who rolled and got more than a 10, that is, more than the lowest possible good roll) might reveal something that you did not notice automatically (with or without effort).
Most locks can be picked with enough time
A rogue in the party tries to pick a lock. He rolls a d20 and gets a 13 + 2 Dex for a total of 15. The door stays locked.
The rogue can simply try again for a higher roll, unless the DM rules that there was some cost to the failure (and with an initial roll of 13, that would be unusual unless the lock was also trapped).
Indeed, in many situations the rogue can simply say "I will keep trying until I pick the lock," and the DM will say how long that takes.
Under "Multiple Ability Checks"(DMG, page 237):
Sometimes a character fails an ability check and wants to try again. In some cases, a character is free to do so; the only real cost is the time it takes. With enough attempts and enough time, a character should eventually succeed at the task. To speed things up, assume that a character spending ten times the normal amount of time needed to complete a task automatically succeeds at that task. However, no amount of repeating the check allows a character to turn an impossible task into a successful one.
Thus, if a character has any chance of succeeding at a check, the DM estimates how long one check would take, multiplies that by ten, and declares the character to be successful after that amount of time. 'Any chance at succeeding at the task' is most naturally interpreted as 'if the thief had rolled a 20'. So in the case of your thief with Dex +2 and, as Dale M points out, most likely proficiency in Thieves' Tools, you can automatically be assumed to have a 24 with enough time. For a thief with slightly better Dexterity, or a party with access to the guidance cantrip, that can reach a 25, or a Very Hard lock.
Now, in your comments you note that the lock in question was on the door of a noble, so time itself may have been a cost - the thief may have been discovered by guards before the lock was picked, or may have been heard by someone within the bedroom. But when time is not an issue, automatic success without a roll is available even for low-level characters attempting Very Hard tasks.
10 is not a bad roll - but 9 is.
What's considered a bad ability check roll? Is 10 a bad roll?
I expect you already know that things your characters attempt that have a chance of success or failure are typically resolved with a d20 roll, with 1 representing the worst luck possible (sometimes a critical failure) and 20 the best luck possible (sometimes a critical success). In between these, 2-9 is considered poor luck and 10-19 good luck, with the break point occurring between 9 and 10. As far as I know, this is not spelled out explicitly in the rules, but it is implicit in a few places, such as in Death Saving Throws (emphases mine):
Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life. Unlike other saving throws, this one isn't tied to any ability score. You are in the hands of fate now, aided only by spells and features that improve your chances of succeeding on a saving throw.
Roll a d20. If the roll is 10 or higher, you succeed. Otherwise, you fail.
Another place the 9 vs. 10 dichotomy is implied is in the rogue ability, reliable talent:
By 11th level, you have refined your chosen Skills until they approach perfection. Whenever you make an ability check that lets you add your Proficiency Bonus, you can treat a d20 roll of 9 or lower as a 10.
Your talent is so reliable that you actually cannot make a 'bad roll' - defined as 9 and below. You might not roll high enough to succeed at a truly difficult task, but you are guaranteed a roll that is at least good, defined as a minimum of 10.
You may notice that if 1-9 is bad luck (and this happens 45% of the time) and 10-20 is good luck (and this happens 55% of the time), then a 'good roll' is more probable than a 'bad roll'. This is intentional - the PC's are heroes, and have the odds tilted in their favor.