No, the back end software is not openly available.
However, adding support for (self run) insight servers (and later maybe toshi and libbitcoin as well) is in the works.

It all depends on your phone....

Is it rooted, do you have an antivirus and or anti-malware app on it?

From my experience MyCelium is a solid app that does what it says. I'm no expert but it seems to have excellent security. With that said, I'm not one to tempt fate thus the reason why I keep the bulk of my coins in a Trezor wallet with just some small amounts for daily use in MyCelium.

Too many to recommend and they are all good, best to search the forum. You should be fine with MyCelium though.

Personally use a Trezor hardware wallet with all the wallets setup on Electrum.

If you don't download apps on your phone it's going to be tricky installing Mycelium. You could try downloading it on a different phone and transferring the installation file over, but I'm not sure how to go about that.

I have at times kept thousands of Bitcoins in Mycelium and never had it lose any of them. Having said that, I don't think the private keys are encrypted in the phone's storage, so if anyone steals your phone they will be able to steal your Bitcoin balance unless you are able to move it first.

Are there any plans to offer secure encryption of private keys, such that a passphrase has to be entered before private keys can be decrypted? Something similar to what Bitcoin Core offers, where I can unlock my wallet for a specified time period. As I understand it the current 6 digit PIN code isn't an encryption key, and even if it was it is easily brute-force-able.

Is there a step by step tutorial that describes in depth every feature of BTC hopefully in Youtube? im trying to understand how all the features work but I can't find a full tutorial, I understand things better if im looking and hearing them rather than reading a ton of text.
Since its an HD wallet, does this mean that everytime I send a transaction I generate a new address and this supposedly improves privacy because they cant see a transaction history in the blockchain? i just don't get how this works, i have only used bitcoin core.

All the vids you'll ever need: https://bt.irlbtc.com/view/268955.0 (scroll down for explanation vids). And some more for good measure: https://www.youtube.com/channel/UCgo7FCCPuylVk4luP3JAgVw

Info on HD wallets: https://en.bitcoin.it/wiki/Deterministic_wallet

Two questions feature requests for my absolute #1 favorite wallet app

1. I noticed in 2.4.4 you updated the transaction fee calculation. Even on low-prio, it currently applies over 0.08 m฿ fee. Until the previous version, the 'economic' mode used to do 0.01 m฿ fee. I have done hundreds or even thousands of transactions like that, and never had a single problem with any of them. Obviously, during the spam stress test periods, it could take several hours before it gets confirmed, but in most cases that is not a problem (otherwise I would have used a higher fee).

I understand why the new algorithm is better, and adaptive, based on the current mempool size and everything. But still, could you please consider to also keep the old fee structure at least an option? I.e. something like "smart fees" (the default) which uses your new algo, and "fixed fees" (like it used to be) with fixed 0.01 m฿ or 0.1 m฿ for economic and normal. Or just one extra option in addition to the current fee settings, called "low fixed" or "very low prio" or something, which does 0.01 m฿.

2. When viewing transaction details, you can visit the transaction on a block explorer. This seems to always visit blockchain.info. Especially with all the bugs and security issues they are struggling with, but also to avoid too much of a monopoly or single biggest player, is it possible to add more block explorers there, and let me choose (through a setting) which it uses by default? Some block explorers that I'd like to use instead of blockchain.info are: blocktrail.com, blockr.io, smartbit.com.au, bchain.info, blockchains.io

Thanks for your consideration. ♥

Thanks for all of your reply guys. I will use Mycelium since my phone is not rooted I think its safe for me to use, I don't have plant to store my btc on Mycelium wallet since I will transfer it on my main wallet and sell it. Maybe I can use Trezor in the future if I plan to keep my btc's for a long time.  

Will you add support for other currencies than USD on coinapult? (Ex: EUR...)

Make a second account with just one address and use that account exclusively for message signing?