SOLVED. This function: (Where only last teleport works)
# Multiple teleports in single function
tp @p ~1 ~ ~
tp @p ~ ~1 ~
tp @p ~ ~ ~1
Should look like: (Where all teleports work)
# Multiple teleports in single function
execute at @s run tp @s ~1 ~ ~
execute at @s run tp @p ~ ~1 ~
execute at @s run tp @p ~ ~ ~1
So, was actually my problem. Please close this report.
The fix is posted in description above.