Sadly FFA and TDM are the most targetted by actual hackers of any game mode, since they don't have to concentrate on objectives and just kill kill kill... I'll admit there are better players but most often hacks are identifiable if you know what to look for... you will learn who is and isn't hacking in games after awhile... you'll just know when the script kiddies are in bed and you perform better for like an hour then you'll know when they wake up and start all over again...

You may be experiencing hacks but most likely you are experiencing lag.  In other words, they seem superfast and can insta kill you because they literally are a good second ahead of you in the game.  MW3 has a rather faulty lag comp system which was supposed to purposely delay players with better signals with the idea of leveling the playing field but ultimately all it did was slant the playing field deeply in favor of people with worse signals.

Now to the game itself.  You've already unlocked the heartbeat sensor but about lvl 78 I believe is where you can unlock the portable radar.  It's basically a localized UAV which on some maps can cover a good portion of the map and it's effect will be seen by everyone on the team that's using it.  It's very common in FFA for portable radars to be down.  Although in FFA only the guy using it will see it's effect.

My best advice to a guy starting out would be to run Assassin.  The enemy will still hear a beep when you enter the range of the portable radar but they won't get a red dot and that is bound to help to keep you alive for longer periods of time.

Also since you are playing FFA a lot, I would suggest getting familar with the SMGs.  All but the MP7 are best used when hipfired which can give you a jump on the enemy by not having to ADS.  SMG's are short to midrange weapons for the most part but often in FFA that's exactly the type of engagements that you are encountering.  So they work out well.

You're level 40...

Although there are a lot of hackers, I would say that you are likely just not up to the same standard as players that have been at this for almost an entire year.

I get called a hacker multiple times daily in FFA and TDM.  Yet, I have no bans on record in 8 years with the same steam account.  I have played every COD game, and have just learned how to best manipulate the perks that they have given me to use in the game.

For example:

Sit Rep Pro.  Most people (even one's that have played the game for a long time) don't realize what this perk does.  When you unlock the pro version you can hear other player's footsteps a long way off.  The ability to pin point the location of these footsteps is largely dependent on how good your headset is.  Many serious players run high end headsets - yes this makes a HUGE difference.  I have used 5 different headsets vearying in price and quality and I can confidently say that there is a massive advantage here.

Specialist "kill streaks":  I also use a very strange specialist build.  Specialist allows you to unlock other perks as you kill other players or take objectives.  I run dead silent pro, stalker pro, and marksman pro for specialist.  My main perks are scavenger pro, assassin pro, and sit rep pro.  Once you get 8 kills without dying you unlock and use every perk until death.  This is a MASSIVE advantage if you can do this.  Keep in mind, the more perks that have the "pro" version unlocked, the more deadly this build becomes.

These things combined with play style give the seasoned player the one up in any FFA or TDM.  My KDR in FFA is around 2.0 and my TDM kdr is around 1.65 (avg weekly over the last 2 months is 2.4)

If you really want perspective look at it like this...you are level 40.  I am prestige 20, level 80.  That makes me technically...level 1600.  I should boot stomp you every time.

That said, there are plenty of hackers out there right now.  Look for people pulling off nothing but headshots, or the very blatant bullets coming through walls from that person all the time (keep in mind that uav and sit rep pro can sometimes get you walled legitimately).

Pickels