1. I don't want a contact to know I'm on WhatsApp. Can this be done?
No.
Even when you block a contact, they'll cotinue to have you in their contact list because they presumably still have your number in their phone book. The only way you won't show up is if the other person doesn't have your phone number saved in their phone.
The fact that you can't see that person on the contact list doesn't mean they can't see you, and vice versa. Whether or not you can see the contact doesn't make a difference: If they have you on their list, they'll see you. And you can't clear their list remotely.
If you suspect that they don't have you, don't give them your number or send them a message. When you add someone to your contact list, you'll see them on WhatsApp, but if the other person doesn't have your number, they won't see you until you contact them.

2. Can I appear as invisible?
Yes.
On Android, you either need to activate airplane mode before you read a message, or turn WiFi and Data off. That will prevent the last seen message from being updated, and you won't show up as "Online".
It's known as the poorly named "invisible mode", which really just disconnects data and WiFi. To activate the "invisible mode" on WhatsApp for Android easily, you can use WhatShadow, an accessory that turns off WiFi and data.
On iPhone, the issue is much simpler: just go to chat options and in advanced options, disable "Last seen online." Note that the changes can take up to one day to apply, so don't start reading straight away.

3. If someone is given my old number, will they be able to download my messages and see my contacts?
No.
They won't see contacts or be able to access old chats - that data is saved on your phone - but they can receive messages sent to your old number (without knowing who sent them).
WhatsApp gets its contacts from your phonebook, so it's unlikely that the person taking your old number will have the same contact. On the other hand, if the other person has WhatsApp installed, your friends will see that this person isn't you.
4. Is WhatsApp free or paid for?
WhatsApp is paid for.
It always has been and always will be a paid-for app. It's the only way the application can get away without having ads, something its developers have always fought for.
It's true that the length of the free trial period varies greatly between platforms, but either way, you end up paying very little to use the service.

5. Is there a way to delete contacts forever?
Yes.
To delete contacts, simply remove them from your phonebook. If you don't want that person to be able to message you either, you'll have to block them.
But remember, if they have you in their phonebook, then they'll still see you on their contact list, but won't know if you're online or not.

6. Is there any way to tell if someone has read my messages?
Yes.
Theoretically, there is no way to know for sure if someone's read your message, but the introduction of the double blue check mark indicates just that. Here's a quick summary of what WhatsApp's icons mean:
Clock: The message hasn't left your phone yet, meaning there's either a problem with data or Wi-Fi connection. You can delete the message before it's sent.
Single grey check mark: The message has been delivered to the WhatsApp server. It's left your phone, but hasn't yet been received by the other person.
Double grey check mark: The message has been delivered to the other person's phone, but they haven't necessarily read it yey.
Double blue check: A new icon that indicates that the message has been read (or at least opened in your conversation) by the recipient.
In addition, if you hold down on the message and tap Info, you'll be able to see what time the message was delivered, and what time it was read. Remember though, that just because the message is 'read', doesn't mean that the person has definitely read the message. Chances are they have, but they may also have left open your chat and gotten the message without actually reading it.
7. If I block a person, can they tell?
No.
A common symptom of blocking is that you can't see the "last seen" or "online" status. Be warned though, if the other person uses WhatsApp on an iPhone, they may have turned off this feature.
Another result of blocking is that messages are left with only one tick and never get a second, although this could also be due to other causes, like the phone being turned off or lost.
If you know it's neither of these reasons, the chances that you've been blocked are hight, but it's still not 100%. If you really wanna know, trying sending an SMS or calling the person.
8. Is there any way to silence a group and receive the messages after?
You don't need to.
When groups are muted, the messages keep coming, only you're not notified.
To silence a group, just tap the menu button (on Android) or info (on iPhone) and press "Mute" or "Mute Group". It's a useful feature to prevent your phone from vibrating incessantly.
9. When you invite someone to a group, will they be able to read previous messages?
No.
When entering a group, a person can only read messages sent from that time. They don't have access to the history.
10. If I delete a message or photo on my phone, is it deleted from the other person's phone too?
No.
If only it were that simple. As it turns out, a message, photo or sound sent through WhatsApp will be delivered as soon as the first green tick appears.
The only way to delete a message before it reaches the recipient is to delete it before it reaches the server. Turn off the data connection and delete the message while it still has the clock icon beside it.

Is there a way to know if my girlfriend is monitoring my msg??

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Tydies:
Is there a way to know if my girlfriend is monitoring my msg??

Yes there is a way but this one pass WhatsApp. Ask ifa instead