¡Gracias Tomisimo!
That' s very good to know, this would be typically one of those occasions where I am mixing up these words due to the subtle differences.
Ok as said before I will try to make a few brief sentences with these different words (especially propio) to see if I am any closer to grasp the differences.

As always I would welcome any corrections and comments/ help!
Mismo:
1. Ya he visto yo mismo como él ha intentado seducirla!
(I have already seen for myself (with my very own eyes?) how he tried to seduce her.) (Sentido: self/myself)
2. Mi hermana e yo son nos paracemos mucho - ¡ es decir que nuestras caras (rostros???) son parecidas pero no las mismas!
(My sister and I look a lot alike - meaning that our faces are a lot alike but not the same!) (Sentido: alike, the same)
Or would you be more inliclined to use ' iguales' in this case? Is ther a difference in the use of 'la cara' and 'el rostro' ? I heard 'rostro' when referring to the serene face of a buddha statue so I am not sure if this is also used for humans?
3. ¡Lo he hecho yo mismo, porque quise estar segura (quise asegurarme?) que nada hubía (hubo??) sido olvidado!
(I have done it myself because I wanted to be sure that nothing has been forgotten).
Por mi cuenta:
4. Vine a la fiesta por mi cuenta aunque no había estado invitado .
(I came to the party on my own (initiative) although I had not been invited.)
Sóla:
5. Vine a la fiesta sóla porque ninguno de mis amigos tuvo tiempo para acompañarme.
(I came to the party (all) by myself/ alone because none of my friends had time to come along with me/ accompany me.)
Ps: I am assuming in this case it is 'ninguno' and not 'ningún'?
Propio/propia:
6.Vine a la fiesta en vestido propio para ver porque se la considera tan especial por algunos.
(I came to the party in appropriate clothes/atire to see why it is considered so special by some).
7. ¡No, mi propia casa no es paracida a la suya! Vivo en un piso modesto ya que por el contrario ella vive en un verdadero palacio!
(No, my (own) house is not like hers! I live in a modest flat whereas she on the other hand lives in a real palace!)
8. Mi propio deseo sería de viajar (estar de vacaciones?) en America del Sur, pero a mi novio no le gusta la cultura antigua ni el clima húmedo tropical.
(My own wish would be to go on holiday to South America, but my boyfriend does not like the ancient culture nor the humid tropical climate.)
9. Esta baila muy complicada pertenece a este región propia de Indonesia.
(This very complicated dance belongs to this characteristic/specific region of Indonesia).
--> Having some doubts about this one.
Thinking it might be more usual or logical to use 'caraterística' or 'específica' in this case, to avoid confusion maybe?
I understand 'propio' has this meaning but I have some trouble putting it into a good, natural sentence.
Also I am not sure if 'partenecer' is the right word, as it means belonging as in posession I think, and I mean it in the sense of 'is part of this region'?
10. Estes son los libros propios de la biblioteca de la universidad
.
(These are the books belonging to the library of the university).
Ok I'll leave it at this for now because it's better to perhaps try some more after feedback I think.

I have a sneaky suspicion that I have made 'unnatural' sentences with 'propio' eventhough I think I understand the meaning of it in general. If this is the case maybe someone can give me some pointers or ideas on how to improve it? I would really appreciate it!
¡¡Gracias!!