Prophecy Char and Faction Points

If I have only a prophecy campaign, can I still get faction points?
If not, is there a way to collect faction points?
I need to unlock weapon upgrade using faction points.

"unlock weapon upgrade using faction points"
....You mean balthazar's points? If yes, then all you need to do is pvp to get them points. It will only unlock skills, weapon mods etc for pvp chars and heroes btw.

Is there a better way to unlock weapon mods/upgrades for PvE beside hunting?

GuildWars FACTIONS doesn't refer to Balthazar faction but to kurzick and luxon faction. In all campaigns you need balthazar faction to unlock weaon upgrades, runes, heroes etc. This also counts for Tyria. You can earn faction by playing in the Random Arena's or any other kind of PvP. You can unlock things at a Priest of Balthazar.

EDIT: Ooh, when i submitted the post, I saw you just posted again in the thread.
you can use balthazar factions to unlock things in PvP.
you can identify magic items to unlock things aswell in PvE. When you see an item with the rule: "unidentified"
you can use an identification kit to unlock the upgrade. To salvage the upgrade off you must use an EXPERT or SUPERIOR identification kit. the upgrade will then appear in your inventory. For more info see Guildwiki:
http://gw.gamewikis.org/wiki/Main_Page

Well, since you only have prophecies, don't worry about the heroes (which require Nightfall IIRC.)

You use Balthazar Faction to unlock skills and upgrades for your PvP characters (Priest of Balthazar NPCs have all these things for you to unlock.) And yep, these unlocks are only available for PvP characters. You don't get the skill/upgrade on your PvE characters this way.

You earn Balthazar Faction by playing PvP.

The Factions campaign, Chapter 2, has two other types of faction (Luxon and Kurzick) but they're used for completely different stuff that you don't need/can't use unless you have Factions anyway.

EDIT - regarding the above question about unlocking stuff for PvE ... no. PvE characters don't get the unlocked upgrades from faction rewards. Here's an example. You unlock a +30 hp sword pommel with faction. Now any PvP character you have can use a sword with a +30 pommel. If you want a +30 pommel for your PvE character's sword, you have to find one in PvE. The only way to get them in PvE is to find one yourself (hunting) or to trade with another player for one.

EDIT 2 - regarding the question below, you'll find some people that swear certain things have a higher drop rate in some places than others. Check the Farming subsection of the PvE forums here, The Campfire. Personally, I'd recommend a different route. If there's a specific thing you have your heart set on, shop around and buy it from another player. If you're willing to farm like mad for one particular thing, just farm like mad for wealth in general instead. Once you have enough gold in game, buy the thing from someone selling it. If it's a significant investment for you, I'd recommend checking out the Auctions and the trading forums (Ventari's) here. You can see what this particular mod usually trades for, and maybe you'll even find one you want to buy. Always a good idea to have something of a ballpark price in mind before trading with strangers.

Thanks guys for the info. I do have another question though.
Is there any info on the specific place where certain weapon upgrade will be dropped (like in D2X)? or does it the same regardless of what type of char, level, location, number of people?

I want to do hunting now since I cannot unlock "weapon mods" through the balthazar faction point but I want to do it efficiently and not just randomly. In order to do this I need to find the information about the hunting place, boss type, etc. Any info is appreciated.

No. There is no specific locations in which weapon upgrades drop. The only way to unlock a weapon upgrade without using faction is to identify (using and ID kit) a blue, purple, or gold weapon. After doing that you will unlock whatever mods the weapon had on it.

But if you are interested in getting mods to put on weapons for a PvE character and not just to have them unlocked on your account I would suggest looking into Green weapons. They come with mods already on them and are relatively cheap.

You don't unlock weapons for PvE, you loot them there. Unlocking weapons gives you no advantage in PvE.