Note that to get command line on iPhone, you need to jailbreak it first.

iPhone

To call: install sbutils from Cydia and type this on command line:

sbopenurl tel:+79123456789

To SMS: install biteSMS from Cydia and type this:

/Applications/biteSMS.app/biteSMS -send -carrier +79123456789 'hello'

Note that I tried some other application, but it don't work with Cyrillic (and probably other non-ASCII) letters

Android

To call:

am start -a android.intent.action.CALL -d tel:+79123456789

To SMS: install shellMS from F-Droid and follow its instructions, like this:

am startservice -n com.android.shellms/.sendSMS -e contact +79123456789 -e msg 'hello'

Note that I tried using some native intent, but it didn't even fill in the message.

To turn screen on or off, emulate pressing "power" button:

input keyevent 26

To check if screen is on or off (note that you need Unix tools for this):

dumpsys power | grep blanked | sed 's/.*=//'