Here is a good list of choices for substitutions: http://foodallergies.about.com/od/cooking/p/cookingwoonions.htm.
The thing I found interesting though, is what it says about Garlic and Onion powder:
Garlic powder and garlic salt are made from dehydrated, finely ground garlic. Onion powder and salt, likewise, are made from onions. These products are not suitable for anyone with a true allergy to either of these foods. However, some people who do not have true allergies to these foods and avoid garlic and onions due to gastrointestinal upset find that these products do not aggravate their symptoms, especially if used in small amounts.
So the question becomes, is it an actual allergy? You may want to check with the doctor on that one.
Here's their list of substitutions:
Fennel has a licorice-like taste but onion-like texture. Try it with chicken or fish.
Celery is among the most common aromatics.
Bell peppers are often used in Cajun cooking. Green peppers and celery are a good base for rice dishes or savory stews.
Carrots are used as an aromatic in French cooking in combination with celery.
Celeriac, or celery root, is the knobby root of one variety of celery. Peeled and diced, it can be used as an aromatic in sauces or
stews.
Peppercorns: white, pink, or Szechuan pepper can add different flavors to your cooking.
Cumin's distinctive taste that may work well in some recipes, especially where garlic is used raw.
Horseradish, freshly grated, can add some of the pungent notes you might otherwise lack.
Ginger and galangal have distinctive flavors but may be useful in stir-fries as aromatics.
I have always wondered how in anglosaxon speaking countries, people think that "mint" is always the same as "mint", just because it has the same name. In fact, spearmint tastes as different from peppermint as thymian from oregano. Almost all cooking recipes I know of are meant for spearmint, except for some sweet applications. All mint tea I have encountered is made from peppermint, not from spearmint. So while you can use dried spearmint instead of fresh mint, using mint tea is a bad idea, unless yours happens to be an exception made from spearmint.
You could try finding out if a herbs seller has dried spearmint, but you must remember that it has less aroma than fresh spearmint. Also, dried mint does approximate the aroma of the fresh one when used as a herb, but when used in big quantities (you mention 1 cup) as a vegetable on its own right, the substitution is much more problematic, because juiciness and texture are much more different.
I don't know about the situation where you live, but spearmint isn't used much in Western countries, except maybe England, so it is seldom available at supermarkets and costs a lot there. A better source are Turkish grocery shops, where it is as common as parsley, and the price is comparable. If there are Turkish shops nearby, it is definitely worth trying to find it there.
For a longer term solution, it might be a good idea to grow your own spearmint in pots. The plant is quite unassuming and easy to care for, and a kitchen which smells of fragrant herbs is nicer than one which smells of frying grease or cleaning products.
Best Answer
Any recipe where the water is part of a sauce or is expected to be absorbed (including rice, couscous, and yes, pasta too), you can use stock instead to increase the deliciousness. If you have an opportunity to add flavour, why waste it?
Of course, there are some caveats to consider when making the substitution:
Stock is going to contain a certain amount of gelatin (how much depends on how the stock is made). This is often a good thing, leading to a richer mouth-feel, but if the thickening effect would be detrimental to your recipe, then don't use stock.
Stock can clash with other flavours, although less often than you'd expect, since it's effectively a mega-dose of umami. In particular I'd probably avoid using it in recipes that are either very sour (sour meat is the taste of rancidity and highly displeasing) or very sweet (since the sugar will overwhelm the flavour of the stock). So don't use it in your candies or in your pickling solutions, but any dish based primarily on meats, vegetables, and grains, is definitely fair game.
Because it's a meat product, it has a limited life span. I wouldn't recommend substituting it for water in anything that's going to sit in the fridge for several days and/or be re-frozen, due to food safety concerns.
Oh, and I probably wouldn't use it in baking. The effects of using homemade stock when the primarily role of the liquid is to develop gluten would be unpredictable, to say the least. And somehow the thought of turkey-flavoured cake just doesn't sound very appealing to me.
As for the right ratio - that depends entirely on what went into the stock, how long it was simmered for and whether or not the stock itself was reduced prior to storing/freezing. You're definitely going to want the same total amount of liquid, but if the stock is highly gelatinous then you might want to dilute it, and conversely, if the stock is very weak then you might want to reduce it. There really is no golden ratio, but I'd probably stick with 1:1 for a "typical" stock.