So, if I'm correct, to attack, you would roll your attack bonus, see if it lands, roll to get damage, then roll to see if it's over the enemy's AC. This seems really hard to get to; also, what exactly is hit points max? And Spellcasting ability, and also spell attack bonus?
I get everything else though. Thanks in advance! I'm playing DnD 5e right now.
First, I would suggest you do some quick research into the basic rules of D&D 5e. The game's publishers have an official PDF of some rules to get you started. You should look at that.
I'll try to address all the terms you asked about:
Attack bonus: When you try to attack an enemy, you roll a d20 and add your Attack Bonus. This is usually for non-magical attacks. If the sum of the d20 + Attack Bonus is greater than or equal to your enemy's AC (Armor Class), then the attack is successful.
If you're using a ranged or finesse weapon, then the Attack Bonus includes your Dexterity modifier. Otherwise it probably includes your Strength modifier. If you're proficient with the weapon, then you also add your proficiency bonus to the attack roll.
Example: If you're proficient with a scimitar, and you're using it as a finesse weapon, then your attack roll will be a d20 + your proficiency bonus + your Dexterity modifier. If the sum is greater than or equal to your enemy's AC, then the attack hits and you can roll damage.
Damage: When you make a successful attack, you roll damage. Depending on what kind of weapon you're using, this value is a die roll plus a modifier: For ranged weapons and finesse weapons, you add your Dex modifier, otherwise you usually add your Strength modifier. Don't add your proficiency bonus. The enemy takes this amount of damage, and it is subtracted to their hit points.
Example: If you use the scimitar as a finesse weapon, its damage is normally 1d6 + your Dexterity modifier.
Hit points max: This is the maximum number of hit points (HP) you have. It changes if your Constitution modifier changes. Your max HP may also increase when you level up; the amount you gain will depend on your class and Constitution modifier.
Spellcasting ability: If you have levels in a spellcasting class, then you use one of your ability modifiers. Wizards, Eldritch Knights, and Arcane Tricksters use Intelligence. Clerics, Druids, and Rangers use Wisdom. Bards, Paladins, Sorcerers, and Warlocks use Charisma.
Spell attack bonus: This is very similar to Attack Bonus. But, rather than using it when attacking with a weapon, you instead use it when you cast certain spells. Normally, your spell attack bonus is equal to your proficiency bonus + your spellcasting ability modifier. Note that many spells don't involve attack rolls.
Example: A wizard casts Shocking Grasp against a nearby enemy. The wizard rolls a d20 + their proficiency bonus + their Intelligence modifier. If that sum is greater than or equal to the enemy's AC, then the attack roll is successful, and the enemy is affected by the spell.
No, that's not quite right.
You roll to hit, which is a d20+ to hit bonuses. If that roll beats the targets AC, you have hit and can roll damage, which is based on the weapon and can also include bonuses.
The rest should be broken up into different questions, but in sum they show if your character can cast spells or not, which attribute they use for doing so (eg wizards use Intelligence, clerics use Wisdom), and what bonus applies when casting.
This is all covered in the Players Handbook, and in the free PHB primer online.
EDIT
Expanding for your specific case, you say you want to use a Scimitar. A Scimitar is a "martial" weapon (meaning you can only get your Proficiency bonus if you're proficient in martial weapons, or specifically in Scimitars), and it's also classified as a "finesse" weapon. That means that you can choose to use your Dexterity bonus or your Strength bonus.
Assuming you want to use your Strength bonus (+1 you say) and you are Proficient in Scimitars, as a level 1 Fighter (or really anything so long as you are proficient) you'd roll a d20 to hit, add +1 for Strength, and +2 for Proficiency to get your total score. Therefore if you rolled a 10, your total attack score would be 13 and you'd hit most folks wearing Light armors (leather, studded leather, etc) so long as they didn't have a shield or too good of a dex bonus.
