[SalesForce] Batch – Sending data from one batch to another

I having a little issue to understand the concept of passing params via batches.

I have two batches which I would like to send data between them.

Batch A creates a Map<sObject,Set<String>> and in the execute method, I put data in it.

After that, I would like to send this Map to batch B.

1. Should I implement Database.Stateful at this case? I know Database.Stateful used for passing data between executing method of the same batch. for example, counting or sum a field.

Of course if the batch will be split to more than one execute I will need Database.Stateful for adding the values of the different executes to the Map, but do I need Database.Stateful for passing data through different batches?

2. What it means: That Database.Stateful will drastically decrease its performance? How it manifests itself? Only the time of execution?

3. Would be better to save the data in a custom object and in the second batch query the data and use it? (of course it individual, I'm talking when I need to pass a Map of Object with Set ).

4. Assuming that the second Batch (Batch_B) that executed in the finish method is stuck in the queue.
   How the data (Map) is saved for this batch? where it saves the data? How can I know that the Data will not be deleted or override by other batch processes? How many Data can I send and Save?

5. Other Best Practice and Ideas will be much appreciated!

Thanks and sorry for this many questions.

A simple code is posted down below.

BATCH A : ————————————-

global class Batch_A implements Database.Batchable<sObject>, Database.Stateful {
    Map<Sobject,Set<String>> myMap= new Map<Sobject,Set<String>>();
    String query;

    global Batch_A() {

    }

    global Database.QueryLocator start(Database.BatchableContext BC) {
        query = 'SOME QUERY'

        return Database.getQueryLocator(query);
    }

    global void execute(Database.BatchableContext BC, List<Sobject> scope) {   
     // After a loop throtgh scope and its related : 
          myMap.put(Sobject,set<String>);

         }

    global void finish(Database.BatchableContext BC) {
        Id batchJobId = Database.executeBatch(new Batch_B(this.myMap), 200);
    }

}

BATCH B : ————————————-

global class Batch_B implements Database.Batchable<sObject> {
    Map<Sobject,Set<String>> myMap = new Map<Sobject,Set<String>>();
    String query;

    global Batch_B (Map<Sobject,Set<String>> mapValues) {
        //Check the values that sent from Batch_A
        System.debug('mapValues In Constructor -> ' + mapValues);
    }

    global Database.QueryLocator start(Database.BatchableContext BC) {
         //Some Start logic
        return Database.getQueryLocator(query);
    }

    global void execute(Database.BatchableContext BC, List<sObject> scope) {
       //Some Execute logic
    }

    global void finish(Database.BatchableContext BC) {
         //Some Finish logic
    }

}