I have read that fees when sending from segwit addresses are lower than fees when sending from legacy addresses. Is it true? If so, what kind of differences are we talking about?
A standard (legacy) transaction has the following size:
count of inputs * 180 + count of output * 34 + 10 = 224 +/- 40 byte
With segwit tx's the size is composed of:
count of inputs * 148 + count of output * 34 + 10 = 192 +/- 40 byte
Generally, your TX will be 32 bytes smaller per input.
What about the estimatesmartfee and settxfee commands? Right now, when the network is quite busy we had fees of 20-25 EUR to send out from legacy addresses (to be confirmed in time).
Do we have to set the same transaction fees (by settxfee) as before?
Generally fees are set in sat/B.
Since the only "fee-advantage" you have with segwit are the smaller transactions, you can just proceed with taking the same sat/B fee, and paying less.
Is this a correct assumption that the same transaction initiated from a segwit address is ALWAYS lower in size than the same transaction initiated from a legacy address?
Yes.