The definite article “la” is used for essentially two purposes, the determinating fonction and the generic one, the first use being the most common.

If you are talking about a set of toys you have to say “de” (no article), because you are not talking about one doll in particular, nor a specific doll but instead you are talking about the purpose of the house, the type of the house: it’ a doll’s house, it’s meant for dolls; (same thing in English, the article “a” is the determiner of “house”, not “doll”.). You use no article at all in that case in French.

A firm that makes dolls and sells them can call themselves “La maison de la poupée” because in that case “maison” means “firm” or “business”, and “le” is used generically.

In English you use a plural or the singular with “the” for this generic function; in French you do to, except that you must use the article in both cases;

• The lion is a ferocious animal. or Lions are ferocious animals. (same meaning)
  Le lion est un animal féroce. or Les lions sont des animaux féroces.

If you are talking to a child playing with toy houses and a doll and that you refer to the doll, then you have to use the article “la” because you are not talking about any doll but precisely that the child is playing with : « la maison de la poupée ». (It’s the same thing in English; you say “the doll’s house” and in that case “the” is the determiner of “doll” and not “house”.)

It’s the same for “visa”. When you talk about the type of demand you use no article;

• une demande de visa, la demande de visa
• une demande de carte de crédit, la demande de carte de crédit
• une demande de permission

If you are talking about a particular thing, then you use a definite article.

• la demande du visa
• la demande de la carte de crédit
• la demande de la permission

a few examples with “tasse de thé”

If you want just tea as it is served to anyone else, you say “de” : « je veux une tasse de thé. »; but if you want a specific type of tea and have to specify it in the same phrase , you use “du”;

• Je veux une tasse du thé que vous avez servi à ma grand-mère hier.
• Je veux une tasse du thé vert dans ces boites jaunes.
• Je veux une tasse du thé indien. (l’indien, pas le chinois)
• Je veux une tasse de thé indien. (la sorte est le thé indien mais on n’insiste pas sur le fait que d’autres sortes sont offertes.)

a detail

“Je fais une demande du visa?” is possible but there is rarely a context for this construction; usually you say “Je fais la demande du visa ?”. This is so because there is usually just one single application to be put in for a given visa and as it corresponds to a given visa it is specific; why is “une” usual with “de visa? It is so because you are talking about a type of application and not one for a specific visa (even if you have a specific visa in mind).