First off: I strongly suggest you use JSON to store your data. Then use AJAX to load the file and parse its contents with JSON.parse() to get the resulting JavaScript object.
Your example could look something like this:
[{
"Tag1":["Tag1","info1","info2"],
"Tag2:"["Tag2","info1","info2"]
},
{
"Tag1":["Tag1","info1","info2"],
"Tag2:"["Tag2","info1","info2"]
}]
You would then parse the JSON like so:
var dictionaries = JSON.parse(jsonstring);
As for your question regarding the manipulation of the file, this needs to be done with an API. You will need to handle this server side (in PHP), as you do not want to give the client (or really the rest of the world) access to your Dropbox account. This is probably not as straight forward as you'd like. However, this way you can verify that what you are storing in the file is valid and won't cause a mess when someone else is trying to access the (possibly corrupted) file.
See: Using the Core API in PHP.
However, I believe what you really want is a simple JSON DB. A quick search turned up TaffyDB. There are probably other ones. I have no experience with TaffyDB but it doesn't look too difficult to use and it's widely used.
However, if this is something multiple people will be using at potentially the same time, I strongly suggest you invest the time needed to make a good and most importantly SAFE solution using a reliable database (MongoDB, CouchDB, or any other document based database).