If you're on the desktop site, there should be a bank of characters under the text box that you can click on when you're doing a lesson. If you're on a mobile device, all you need to do is press and hold the letter until a little menu pops up.
But if you want to type smoothly on your non-mobile computer, there's this little program I use on my PC. http://www.spanishdict.com/answers/166839/how-do-i-put-accent-marks-on-my-computer It integrates seamlessly, so you just type a simple key combination and there's your accented character.
No, unless you consider the Scots-English "loch" (lake).
You can check out this interactive IPA chart for help. The symbol you're looking for is /x/ -- it's the unvoiced velar fricative. The IPA is organized along the Y axis by manner of articulation and along the X axis by place of articulation, and paired by voiceless/voiced.
You can pronounce /k/, so you have that place of articulation down. And you can pronounce /f/, so you have that manner of articulation down. Now you just have to practice the intersection.
Consider the difference between /t/ and /s/. That is exactly the difference between /k/ and /x/.
Roghchlár is a list of choices, as in a computer menu. A food menu is biachlár.
For "Irish" as an adjective, Éireannach is probably your best bet - An Biachlár Éireannach. If you were specifically creating a menu of dishes sourced from Ireland, Biachlár na hÉireann might do - it can be read as "Ireland's Menu" or "The Irish Menu", a slightly different meaning, indicating possession.
Shouldn't this be in an exercise like 'food' and the exercise rather consist of things like hello, goodbye, how are you, etc?
Your understanding is incorrect.
Irish doesn't use an indefinite article ("biachlár" can be either "a menu" or just "menu"), but it has 2 definite articles - "an" for the singular definite article ("an biachlár" - "the menu", and "na" for the plural definite article ("na biachláir" - "the menus").
English uses "the" for both singular and plural definite articles ("the menu", "the menus"), and uses "a" for the singular indefinite article ("a menu", but doesn't have any plural indefinite article ("menus").
"an biachlár" means "the menu".
(This is just the nominative case - it's a bit more complex when you include the genitive).