First, for Reference, a zoomed-in segment of the 4e character sheet available for download on WoTC's site.
Your Stats from your Standard array Go in the Score box
The Score is the number coming from the Array (or total via pointbuy) such as 16, 12, 8 etc. By RAW rules you cannot have more than 1 stat lower than 10 and that one stat can only go as low as 8.
Ability MOD is short for Modifier. It is derived from the ability score.
To calculate an Ability mod: (Ability Score - 10) / 2 = Mod. Always round down. For example a score of 16 would equal a Mod of 3, a score of 15 would equal a Mod of 2.
Mod + 1/2 Level is the number you use for skill checks
When you have no appropriate skill your DM will tell you to use the Stat that most makes sense. Its simply there as a shortcut to prevent you from having to do the math when it comes up. For example your character is trying to decipher an ancient tome, History is probably the appropriate skill, but you aren't trained so your DM instead has you roll an INT check. You roll 1d20 and add your Mod + 1/2 your level number to your die roll.
Mod means Mod, not Mod + 1/2 level.
Whenever something references Mod, Ability Modifier or (for example) says STR Mod it means the Modifer number only.
Filling out your defenses
You only want to put the ability mod "ABIL MOD" because in one of the boxes you are already adding 1/2 your level, the 10+ 1/2 your level box.
Filling out skill boxes
You would write the mod + 1/2 level number in the box on the skill section of the sheet because skills you aren't trained in by default just use the related Mod + 1/2 your level whenever you would attempt to do a skill test related to it. Again, this is here simply to save you time later.
Your human ability modifier should go in your primary ability score
Which is whatever stat your class uses to make attacks. In your case if you are playing a Bow Ranger that would be Dex and if you are playing a Melee Ranger that would be STR.
Yes your # of Surges is based on your class + Con mod
Certain races & feats can give you more, but in the example you gave, yes the number of healing surges you would get is 7.
Your starting equipment is your equipment you start with at first level. Gaining a level in another class adds no additional equipment.
Player's Handbook errata clarifies this:
Class Features (p. 164). You gain the
starting equipment of your first class only
Another question might be that a level 10 character should have more advanced equipment than a starting one, which is intended to be used by level 1 characters. That's covered in the question What's the starting wealth for higher levels?
5 weapons is correct if you always choose the option with the most weapons. Though this probably isn't the best use of your initial equipment loadout.
You could list them all on your character sheet, but it might be better to note your attack bonus (your strength mod plus your proficiency bonus plus any other bonuses), and your damage modifier (your strength plus any relevant bonuses), and then either write down or remember the die that you roll depending on which weapon you're using.
This is probably easier than writing the same expression down several times with a different die in each one.
There are only limits on what kind of attack you can take with a specific weapon if specified. One such limitation is for two weapon fighting which requires light weapons.