Front right fork, suspension,chain guide

Either or a combination of both. Suspension set up, tyre pressure, wrong tyre size or type, style of riding???
Check your manual for suspension set up details and tyre pressures. Check out your steering head is tightened correctly. There are no leaks from your fork seals and if all is in order try ridind it differently (and safely) on bends.
If you have just got this bike recently, it could just be that this particular bike doesn't suit your style of riding. I have ridden bikes that don't "feel right" to me but other people have no problem with. Maybe let a friend test ride and see what they say.

I think you might be confusing some terminology.

The Front "suspension" is the fork assembly that holds your front wheel and goes up and down. The shock absorber or suspension.

The part in the middle of the bike that the chain changes between 1,2 and 3 gears is the crankset and relates to the front shifting. The shiftlever on the left of the handlebars would be the part that indicates the 1, 2 or 3 numbers.

To get the front derailleur (changer) to shift into the proper gears the cable must be under the correct tension and limit stops adjusted correctly. Shift the lever into the #1 position and check the cable tension. is it very loose? can you wiggle it easily side to side or up and down? if yes, then you need to tighten the cable by loosening the bolt at cables attachment of the derailleur and then pulling out the slack, tighten the bolt again and check your shifting . If that does not work then take the bike into a bike shop and have them look at it, something too difficult to explain may be happening.

Your front fork seal are bad and need to be replaced.
When you loose fork oil, your loosing suspension dampening and only riding on the springs.(POGO)

Replace both front fork seals and dust caps, and put same amount of fork fluid in both forks.

I bought my seals and caps for $30 on ebay, and then took my forks off my bike and took them to a shop and they charged me $75 to do the job.

You can take them the whole bike and they will charge $100 - $150 including parts to do the job.

Stock fork seals will work but if I were you, I woudl take it to someone who has the correct tools take your fork seals out without gouging the fork leg. If your seals are leaking then chances are you're also low in fluid. Your fluid level is what decides how hard or soft your front end is (In addition to fork spring rate).

Make Model
Honda XL 125R Paris Dakar Year
1983 Engine
Air cooled, four stroke, single cylinder, OHC, 2 valves per cylinder Capacity
124 Bore x Stroke 56.5 x 49.5 mm Compression Ratio 9.4:1 Induction
PD52 Ignition / Starting
CDI / kick Max Power
12 hp 8.7 kW @ 9000 rpm Max Torque
10 Nm @ 8000 rpm Transmission / Drive
6 Speed / chain Front Suspension
Telescopic forks Rear Suspension
Swinging arm Front Brakes
Drum Rear Brakes
Drum Front Tyre
2.75-21 Rear Tyre
4.10-18 Seat Height 840 mm Dry-Weight
109 kg Fuel Capacity
17 Litres

front axle installation: looking at the front of the bike:

slide the wheel into position and insert the axle from the left. with axle now through the right hand fork, install nut and tighten the left fork pinch bolts to secure the axle for tightening the nut. tighten the nut to 29.5 ftlbs. and loosen the left pinch bolts. now tighten the right pinch bolts and compress the front suspension while the left (from front) is still loose. now allow suspension to rest naturally and tighten all 4 pinch bolts to 11 ftlbs.
your done.......the axle is tighten against the rotor side and the other fork is then tighten in it's natural position so as not to cause premature seal and bushing failure and increasing stiction.

it sounds like your fork seal has failed,it wont affect your brakes but will make your front suspension feel a wee bit "soggy"and will affect your handling,i would suggest getting the seal replaced as evetually the oil from the faulty seal will contaminate your brake pads that will affect your braking performance,replacing the seal,sooner rather than later ,would be a wise move..hope this helps...cheers

Add more fluid to the front forks, start with one ounce at a time, thats all it is but dont over fill them or your ride will be too stiff.

It can be as simple as a slight burr or piece of debris caught in your seal. You can try a 3x5 notecard wrapped around your fork leg and GENTLY work it down past the seal. Also inspect the fork tube closely and if you can see a visible burr remove it with very fine sandpaper or emery cloth.

If you have to remove the fork because it is leaking elsewhere (and you have checked your drainplug) that is rather involved and requires you to suspend the front of the bike to remove the front suspension. How far apart you take it depends on what you have to fix though.

go here for a parts breakdown
remove your forks and there is a allen screw in the bottom to hold the forks together . when you reassemble make sure you put the corredt weight and amount of fork oil.
later paul