When I try to engage Siri she says she cannot make the connection and I should try again later. I have iOS 10.0.2 installed. I have shut it off and restarted but the problem remains

You can try different ways to update iOS. One of them shows below.

If a message says that an update is available, you could then click "Install Now" button to start to update your iPhone iOS software. Also, you could manually check whether there is an iPhone iOS update or not on your iPhone. The below steps would show you how to update iPhone software wirelessly:

1. Before you update iPhone software via WiFi connection, you need to make sure your iPhone has enough storage and battery to support the iPhone update.
2. Connect your iPhone to a WiFi network.
3. Tap "Settings > General > Software Update" successively.
4. Tap "Download and Install" option when your iPhone has detects an update available. If a message asks to temporarily remove apps because iOS needs more space for the update, tap Continue or Cancel. Later, iOS will reinstall apps that it removed.
5. Then iPhone would start to download and install iOS update immediately. You only need to wait for the update complete.

For more methods, check: How to Update iPhone

The easiest way for most people to update iOS 10 to iPhone is over the air, directly on their device. It's fast, efficient and simple to do.

1.Click Settings, then tap on General
2.Tap on Software Update.
3.Tap on Download and Install.
4.Enter your Passcode, if prompted.
5.Tap Agree to the Terms and Conditions. Tap Agree again to confirm.
6.Tap Install Now to begin the update.
http://www.leawo.org/tutorial/how-to-update-ios-9-2-to-iphone.html

To use Siri, simply hold your thumb or finger down on the power button. You will hear a double tone when it is open. For Siri settings, go to Settings, General, then check for Siri either in the left hand menu (IOS 10) or on the right side menu.

Yes!
Most people are now on iOS 8.4
So.... do you mean back grade? from 8 to 7
iOS 9 will be released in a few days!
https://www.apple.com/ios/

It can be downloaded & installed directly to your iPhone/iPad
Or... as I prefer.....
use my computer running iTunes to firstly Backup the iDevice (using it's USB charge cable)
ITUNES will at this time indicate that there is an update available for your iPad.
Choose to "download only" the new iOS.
If you have other things to do!
Disconnect while the download takes it's time downloading.
Then come back later and plug in USB cable and "Install" the updated iOS.
How to Update iOS Software on an iPad

1. Turn on your device. When you first turn on your device, you'll see "Hello" in different languages. Slide from left to right anywhere on this screen to begin.
2. Select your language and region.
3. Connect to a Wi-Fi network

You need an Internet connection to set up your device. Tap the name of the Wi-Fi network you want to connect to. 
4. Enable or disable Location Services. This setting lets certain apps gather information about your location.
5. Set up your device as new.
6. Agree to terms and conditions.
7. Sign in or create an Apple ID.
If you need to, you can create an Apple ID for free. Or, you can tap Skip This Step to sign in or create an Apple ID later.
8. Upgrade to iCloud Drive.
With iCloud Drive, you can store your files in iCloud and access them anytime on any supported device. Or choose Not Now to setup iCloud later.
9. Set up iMessage and FaceTime. Or choose not now to setup later.
10. Set up Touch ID.
If you have an iPad Air 2 or later, or iPad mini 3 or later, you can set up Touch ID. With Touch ID, you can use your fingerprint to unlock your device and make purchases.
11. Create a passcode.
To protect your data on your device, use a passcode to unlock your device. If you don't need a passcode, tap Don't Add Passcode. If you're using Touch ID you have to create a passcode.
12. Set up iCloud Keychain.
iCloud Keychain keeps your Safari website usernames and passwords, credit card information, and Wi-Fi network information up to date across all of your approved devices.
13. Choose whether or not to use Siri.
Siri lets you use your voice to send messages, schedule meetings, place phone calls, and more. Or choose Don't use Siri to setup later l.
14. Choose whether or not to share app analytics. Choose don't share.
15. Choose display resolution.
16. Start using your device.
Tap Get Started to begin.
Cheers :-) congrats for new ipad and i hope these instructions will help you.

How to configure Siri

1. Launch the Settings app on your iPhone or iPad.
2. Tap on General.
3. Tap on Siri.
4. Tap on Language to change languages and dialects.
5. Tap on Voice Feedback to choose whether Siri always talks back to you, or only when in Handsfree mode.
6. Tap **My Info* to select your Contact card so Siri knows who you are, what your numbers are, and what your locations are. This lets you say things like "Call home." or "Give me directions to work."
7. Toggle Raise to Speak to have Siri pop up whenever you bring your iPhone to your ear, and you're not on a call. This may drain your battery faster than if it were disabled.

http://www.imore.com/how-set-configure-secure-and-start-using-siri#siri-enable

go to settings - general - siri



http://www.imore.com/how-set-configure-secure-and-start-using-siri#siri-enable

you cannot delete them:
there are some core apps belonging to the iOS system and cannot be deleted like 'clock', 'calendar', 'contacts', 'facebook' etc.
- however you may create a folder (unwanted apps) and put them there, then they are at least out of sight and use less desktop space.....
1) Airdrop
2) Apple Store
3) calendar
4) camera
5) clock
6) contacts
7) facebook
8) game center
9) iBooks
10) iTunes
11) mail
12) maps
13) messages
14) music
15) newsstand
16) notes
17) photo booth
18) photos
19) reminders
20) safari
21) settings
22) siri
23) tips
24) touch ID
25) videos
How to create Nested Folders in iOS 7 Video

there are some core apps belonging to the iOS system and cannot be deleted like 'clock', 'calendar', 'contacts', 'facebook' etc.
--------------------------------------------------
core apps:
1) Airdrop
2) Apple Store
3) calendar
4) camera
5) clock
6) contacts
7) facebook
8) game center
9) iBooks
10) iTunes
11) mail
12) maps
13) messages
14) music
15) newsstand
16) notes
17) photo booth
18) photos
19) reminders
20) safari
21) settings
22) siri
23) tips
24) touch ID
25) videos

core apps of iOS which cannot be deleted!
1) Airdrop
2) Apple Store
3) calendar
4) camera
5) clock
6) contacts
7) facebook
8) game center
9) iBooks
10) iTunes
11) mail
12) maps
13) messages
14) music
15) newsstand
16) notes
17) photo booth
18) photos
19) reminders
20) safari
21) settings
22) siri
23) tips
24) touch ID
25) videos
- here are 2 different ways to delete an App:
1) t's easy to delete apps from the iPhone or iPad. Simply tap and hold on any icon for about 2 seconds - see them to start to wiggle and tap the X button in the left corner. that's it.
2) For devices running iOS 5 and later, there is also another way to do this is hidden in the Settings app, in the General tab, under: usage.