I keep reading that you shouldn't use possessive adjecives with body parts and clothing, and my friend that speaks Spanish says he doesn't for body parts, but still thinks it's ok for clothing. So, it got me thinking how can you distinguish who's clothes or body part you are talking about? In all the examples I see for it, they seem to be using object pronouns with certain verbs like gustar and doler. For instance, if I want to say these things

1. I have to wash my hair.
2. I have to wash his hair.
3. Eat my foot.
4. Eat his foot.
5. I eat my foot.
6. I eat your foot.
7. I like my foot.
8. I like his foot.
9. I have to clean my eyes.
10. I have to clean your eyes.

Here is what I have thought up:

1. Tengo que lavarme el pelo.
2. Tengo que lavarse (or maybe just lavar???) el pelo de él.
3. Come el pie de mí.
4. Come el pie de él.
5. Como el pie de mí.
6. Como el pie de tú.
7. Me gusta el pie de mí.
8. Me gusta el pie de él.
9. Tengo que limpiarme los ojos.
10. Tengo que limpiarte los ojos. or Tengo que limpiar los ojos de tú.
First of all, the translations:
1. I have to wash my hair. Tengo que lavarme el pelo.
2. I have to wash his hair. Tengo que lavarle el pelo.
3. Eat my foot. Come mi pie. (Very weird sentence)
4. Eat his foot. Come su pie.
5. I eat my foot. Yo me como mi pie.
6. I eat your foot. Yo me como tu pie.
7. I like my foot. Me gusta mi pie
8. I like his foot. Me gusta su pie.
9. I have to clean my eyes. Tengo que limpiarme los ojos.
10. I have to clean your eyes. Tengo que limpiarle los ojos.

You're right we don't usually use the possessive with body parts, we use articles, but both forms are grammatically correct, (if I say: "me lavaré mis dientes", it sounds very stilted) and with some verbs and contexts it's more common to use the possessive:
Me gusta el color de mis ojos.
Toma mi mano y vamos a caminar.
On #2 and #10, why does it use le for both "his" and "your"? I want to use the informal your, maybe that's what I have to say. So, doesn't le mean his or her? Also, on #2, how can you tell if you say his hair or her hair?

Also, on #2 and #10, could you say instead

Tengo que lavar su/tu pelo.

???

But, then you'll have to clarify who you mean on #2, so I was thinking like

#2. Tengo que lavar el pelo de él.

#10. Tengo que limpiar los ojos de ti.

or maybe Tengo que limpiar tus ojos.

.....................
Sorry, I made a mistake (I won't fix it for the others to see it) for " your" the sentence is:
Tengo que limpiarte los ojos.

Le can mean her or his it is ambiguous. To be more specific, you must say:
Tengo que lavarle el pelo a ella/él.
Tengo que limpiarle los ojos a ella/él.
Also, these verbs can be used without le, so we have:
Tengo que lavar el pelo de él/ella.
Tengo que limpiar los ojos de ella/él. (But the above versions are better).
Finally, as you say, we have these options:
Tengo que lavar(le) su (her/his) pelo.
Tengo que lavar(te) tu (your) pelo.
Nice, thanks.
10. I have to clean your eyes. Tengo que limpiarte los ojos.
This is kinda weird, don't ya think? Like eating your foot or