The best advice anyone can give you is to please stop experimenting and use tested recipes. Particularly for acidified pickles, there are huge numbers of resources out there with tested recipes verified by scientific protocols. (That is, they tried them many times under many conditions and tested stored versions for microorganism growth to verify they are safe.)
The National Center for Home Food Preservation is one place to start for both general information and many specific tested recipes. Many states (particularly agricultural ones) have similar resources online. The Ball Blue Book Guide to Preserving and the Bernardin guidebooks are also classic resources for such information.
From your description, it sounds like you have left unprocessed, unsealed containers out at room temperature. No, this is not a safe storage method. Yes, the acid and salt will likely inhibit botulism growth, but without using a verified recipe and procedure (as mentioned above), you can't guarantee this. Large chunks of food, for example, may not acidify fast enough to prevent botulism growth, or depending on your recipe, some of the vegetables may release a lot of water when placed in brine, which could dilute the salt and acid to the point that nasty bacteria could grow. That's why there's no magic formula that will guarantee safety by telling you X amount of salt or Y amount of vinegar for all foods. Individual recipes need to be developed and tested.
Botulism is certainly not the only dangerous bacteria, though -- Listeria, for example, is a common bacteria that can grow even in mildly acidic conditions and can cause illness in improperly processed foods. Surface mold can also easily grow in situations like you describe, sometimes with serious toxic effects if eaten. With less acidity or sufficiently diluted conditions, all sorts of things could grow. That's why processing with heat is absolutely necessary for safe room temperature storage, to pasteurize and seal the foods from spoilage agents. (Food stored in the refrigerator is a bit different: without processing, acidified pickles may still be safe for several days or weeks, depending on the recipe.)
Use of a verified recipe is also essential for preservation that will include room temperature storage, as you can't guarantee sufficient acidity, salt, etc. without microbiological tests. Food scientists have worked hard to develop such recipes over the past century, since before that canned food made many people sick. If you really want to store food at room temperature, please don't trust any recipe on the internet or even from some book that doesn't come from an organization which actually does testing.
As to what happened with your current batch and what you should do with it -- first, it is possible that some lacto-fermentation went on during room temperature storage, even despite starting with an acidified recipe. Obviously with all the fizzing, some sort of fermentation has happened. Unfortunately, without microbiological testing, you have no idea what sort of stuff you may have grown or whether it is safe. Lactofermentation usually depends on a higher salt content in the initial phase to select for the right sort of bacteria, which then grow and acidify the mixture to the point that nothing bad will likely grow. However, without knowing exactly how acidic your initial mixture was (again, taking into account possible liquid released from the vegetables you added to your brine) as well as actual salt concentration, it's impossible to know whether you had a good "healthy" fermentation or whether you grew something that could make you sick. Many types of dangerous spoilage bacteria don't necessarily produce a smell or taste sufficient to warn you that they could cause illness.
The only 100% safe recommendation at this point is to throw this batch out and start again with a reputable recipe. And if you plan to store at room temperature, please process with hot water accordingly and seal properly. It's possible (given sufficient acidity and salt) that your current batch may still be edible, but no one here can guarantee that.