1) You can read all the latest "events" in the website: https://www.lineage2.com/news Below each image there are color tags that refer to Lineage 2 Live, Aden and Classic versions of the game so you know which article you need to read.
All of the events (paid or free) will require you to kill mobs to get different kind of items as well as different kind of buffs (like XP buffs or buffs that increase your stats) from the NPCs in towns. The two free active events that are currently active with those buffs are https://www.lineage2.com/news/power-of-love-event and https://www.lineage2.com/news/milky-way-event
If you don't kill mobs (monsters) you will not level up.
2) Mana potions aren't available in the game. Feoh (mages) need to kill mobs fast so their MP won't run low. Killing mobs faster requires better gear such as good weapon, gems (sapphire, blue cat's eye higher level) as well as increased attribute attack damage.
3) You follow and complete all the beginner quests till you start the Exalted quests from NPC Lionel Hunter in Heine. Those quests require you to kill 40.000 mobs in the first 2 parts and then this number increases. Every time you complete an Exalted quest you will get different low grade rewards like brooch, dragon shirt, gems (sapphire and blue cat's eye i mentioned above), exalted armor, weapon, dyes and more. A very good start with a nice weapon, armor, jewels and different kind of potions/buffs that give you stats and XP gain is to purchase the Blessed Exalted Armor pack from l2 store. You can check what this pack includes here: https://www.lineage2.com/news/17th-anniversary-store-update or click the L2 store button in the game.
In order to become "stronger" and earn money (adena), first you must spend real money in the game. You can start by purchasing the Blessed Exalted Armor pack (robe for mages/healers, heavy for tanks/tyrrs/iss and light for damage dealers like daggers, archers) to boost your character's stats and then you need to level up. Leveling up your character will boost your stats more and you will unlock new areas like Tower of Insolence in lvl 110 and other limited instances in lower levels. Make sure you do Coal Mines (daily) instance every day with random parties, you will get good xp. Also, leveling up faster will require you to always have VP on (the green bar on the top left corner of your screen). How do you keep this up? Pay real money in l2 store.
The best way to make money in the game is to buy NCoins and sell them. Don't get excited when you see events like this one https://www.lineage2.com/news/love-boxes that's currently active and you think you will get items. It's simple. You will get NOTHING if you open those boxes and you will lose all your money. Better sell them to make sure you'll get adena. This is the best strategy, sell NCoin or boxes and get adena, then buy the item(s) you want directly from other players or by using the Auction House (AH).
Conclusion: Lineage 2 is a game for rich people, also known as "Pay 2 Win". If you spend real money you will take a VERY HUGE advantage (levels and items) over the other players. If you don't want to spend real money, your progress will be slow as hell. Your character must always be on and kill mobs 24hours, endlessly. The game is a mess since there are a lot of items, NPCs, etc. in the game that are outdated. New players will have a very hard time figuring out how everything works. You can do daily dungeons with random players but this requires good items, otherwise don't even think about it.
I hope i've covered everything. If you need anything else, feel free to ask.