does ь here make a softer "s" sound, like in сіль? I cannot hear it neither here nor in Google Translate
Sure it does. In fluent speech this nuances may be blurred
"ь" does not add "s" sound, instead it modifies the consonant before it. In this case: "т" sounds softer.
I guess the asker meant the word "англійську".
Is this phrase correct and normal in Ukrainian? It sounds very "english" to me, or is it just me?
Yep, sounds right to me.