how to concatenate string variables into a third?
You don't need to use {} unless you're going to use bash variable parameters or immediate append a character that would be valid as part of the identifier. You also don't need to use double quotes unless you parameters will include special characters.
x=foo
y=bar
z=$x$y # $z is now "foobar"
z="$x$y" # $z is still "foobar"
z="$xand$y" # does not work
z="${x}and$y" # does work, "fooandbar"
z="$x and $y" # does work, "foo and bar"
simply concatenate the variables:
mystring="$string1$string2"
In case you need to concatenate variables with literal strings:
string1=hello
string2=world
mystring="some ${string1} arbitrary ${string2} text"
echo $mystring
will produce:
some hello arbitrary world text