すみません (sumimasen) is more formal than ほめんなさい (gomen nasai). Use すみません with people you don't know very well. すみません can mean sorry, excuse me, thank you, etc. Use ごめんなさい (and other variations) with people close to you. That's what I know.
Some people said that すみません can be used as a "light apology" as opposed to "real apology" when using ごめんなさい but idk if that's true.
I think someone else can explain this in a better way.
Yeah you've got it the wrong way around.
すみません is the informal way of saying sorry, and can actually also be used as a way of catching somebody's attention (eg, すみません、トイレはどこですか？Excuse me, where is the toilet?)
ごめん is the more formal way of saying sorry, where ごめんなさい is a very formal way of saying it, like as if you've done something really wrong.
"Sumimasen" is short for "it's my responsibility", "gomen nasai" means "I feel bad about it" Sumimasen is what you say to strangers, your teacher, your boss, etc. Gomen nasai, gomen, gomene (masculine), gomena (feminine) etc are what you say to friends, family etc. The shorter versions can also be used jokingly or to tell someone to calm their shit (=well EXCUUSE me!)
To my knowledge, i agree with @JM B Descalso. Sumimasen is the polite version, and should be used in regard to your "higher ups" (eg. Your teacher) and means sorry as well as excuse me. However, saying sumimasen to a friend in place of gomennasai would almost imply that you are not close enough with them to say gomen (I am not 100% sure about this). Here are some scenarios: To your teacher after bumping into them: sumimasen, sumimasem, sumimasen! To your friend after falling on them: Ahh gomennasai, daijobou desu ka? (Daijobou desu ka means are you alright) Bumping into someone at the crowded trainstation: Ahh sumimasen! And ect.
Actually, I think it's hard to compare すみません and ごめんなさい in terms of politeness or informal vs formal. They're just different phrases with similar uses.
If anything, you can only really say すいません is the informal version of すみません, and ごめん is the informal version of ごめんなさい.
Also, I would find it quite strange if a friend said ごめんなさい for anything that other than a serious grievance. And 大丈夫 is transliterated as daijoubu by the way :)
suimasen itself is not informal but a variation of sumimasen that has changed throughout time,you would know that its formal as it is in the "masu" form, the informal for this would be "suman" saying gomensai to friends is not that awkward unless thats how you are used to say with your friends, or the informal way "gomen"
Great question! Between my J3 Eclipse and my iPhone, they are both consistent in having separate spell check and typing dictionaries. Make sure you are installing the 日本語/Japanese input keyboard. It sounds like you do have it installed though. To use the keyboard, you basically write your Japanese in romaji and it is automatically changed to kanji/hiragana/katana (it gives you the option to pick between them as you go).
I spent 3 days just repeating the hiragana exercises. I go through every character and phrase that is presented as an option to check if I remember it. When I consistently make certain mistakes, I take notes and look for those characters/phrases first to comit them to memory. I often google search the grammar and culture behind what I am learning to gain greater depth. It has been almost 6 days for me now and I feel quite confident with my progress. Don't rely on just one source to learn.