RE: Enemy symbols
First, RS1 was a terrible game, and RS2 learned all the lessons about how NOT to be like that game. Don't get scared by the RS1 gif, RS2 is nothing like that.
Then, you shouldn't be running everywhere, but you also shouldn't be walking everywhere. If you're attacked while running, you break formation, but remember running away from battle has a 100% success rate, so if you're stuck, simply run away, initiate combat, and fight. It also works if you're facing a particularly bad opponent (the green hydra comes to mind) to re-roll the enemy.
The game DOES become harder the more fights you do, but it never becomes insanely hard like RS1, and you won't fail quests like in Minstrel Song. Even the worst mob enemies remain manageable if you balance your party well, AND you can run away as long as you didn't get yourself cornered. Don't be too scared to initiate fights, there is no harsh penalty for grinding.
You need to play the game like if you were playing Resident Evil 1. Do not initiate all the fights except if you are grinding XP, money or development in your castle. Spend the first hours of the game understanding enemy movements.
Each symbol moves in different ways: blobs are slow and only target you when you get too close, snakes move towards you for a set distance then stop, goblins walk at random until they see you and the jog towards you, mammals run fast until they see you then sprint, birds fly super fast in all direction...
You need to understand their patterns, walk and stop until you see an opening, and then move around the enemies, run for a short distance (even though you won't see the enemies, if you have studied the composition of the room you should be able to predict where they go as you run) and reach the next door. The player skill you need to develop (and you'll get increasingly better as you play the game) is really the ability to navigate a map. The run is a very useful tool, but it needs to be used sparingly.
The game is built in that optic, as it introduce some other types of enemies (soldiers, ghosts, octopi) gradually during the first part of the game. The maps are also built to incite you to play that way (the Ludon plain allowing you to run around that big rock, or the desert being specifically made to screw you over). You can also gauge the difficulty of an area by looking at the lay-out or enemy concentration. The Jungle, for example, is a very difficult area not because of enemy concentration, but because the layout is made specifically to make it difficult to avoid the fast birds and very slow snakes/plants.
Imagine everything is a room in the Spencer mansion and you'll be fine.
(Note: this is also how you're supposed to play Minstrel Song)