Is there a maximum daily amount of Series 8 Swiss Francs which can be exchanged for current series at SNB in Zurich?

There is no daily limit. After all, Switzerland is well known for not really caring about where your money comes from.

Of course, nowadays there are more anti-money laundering and anti-tax evasion rules, but they are quite relaxed compared to other countries. For example, there is no limit to the amount of cash that you can import to or export from Switzerland and declaration is not mandatory when you enter or leave Switzerland (but the other country can set their own rules).

The mandatory legal duty to establish identity applies to all non-foreign exchange cash transactions over CHF 15'000 in financial institutions. Financial institutions still have the obligation of due diligence for amounts lower than that and must verify identity and other checks if money laundering or terrorism financing is suspected.

In practice, without other suspicion of fraud, money laundering, terrorism financing, beneficial owner not the same as the person carrying out transactions etc., only verification of identity is needed. Other clarifications may be required in case of suspicion. In any case, no daily limit applies.

In its efforts to safeguard the standing of the Swiss financial centre and to fulfil its duty of due diligence, the SNB may make the exchange of banknotes dependent on further clarifications. These may include, for instance, identification of the contractual partner as well as establishment of the beneficial owner’s identity, and additional clarifications.

Suspicions can arise from things like large amount of small-denomination bills, apparent structuring (i.e. appearing to deposit an amount just below CHF 15'000 to avoid financial scrutiny) etc..

In Zurich, is SNB only place to exchange without a fee?

If you do not have a bank account, then probably yes. If you are going elsewhere in Switzerland, SNB has another desk in Bern and partner banks that will also exchange them. You may still find certain merchants still accepting them, but don't count on this.

In Zurich, is SNB only place to exchange without a fee?

No. I tried to exchange an old banknote at a retail branch of the Banque Cantonale de Genève. The clerk told me I'd have to go to the main office down in the center of town ... or to any post office. I went to the nearest post office, where the window clerk exchanged my 100-franc note without asking any questions, without asking for ID, and without any fee.

The post office accepted these notes through October 2021. It doesn't require much time or effort to try, but I suspect that you might not succeed in changing your notes there anymore.

From https://www.snb.ch/en/iabout/cash (emphasis mine):

Banknotes from the eighth series still held by the general public or economic agents, as well as banknotes accepted by the latter, can thus be exchanged at any time and for an unlimited period at the SNB cashier's office in Berne and Zurich or at an SNB agency at their full nominal value. It is important to note that some agencies apply exchange limits.

Many places also accept banknotes from the eighth series for payments into one's own bank or post office account. Financial institutions must exercise the duty of due diligence in connection with combating money laundering and terrorism financing.

So without a bank or post office account an SNB cashier office or agency (selected cantonal banks) is the place to go, and the cashier offices will not apply exchange limits.

More details are found in the Instruction sheet for exchanging recalled banknotes. :

In its efforts to safeguard the standing of the Swiss financial centre and to fulfil its duty of due diligence, the SNB may make the exchange of banknotes dependent on further clarifications. These may include, for instance, identification of the contractual partner as well as establishment of the beneficial owner’s identity, and additional clarifications.

If you have any specific questions, please contact the SNB Cashier’s Office in Berne directly (+41 58 631 07 57 or bargeld@snb.ch).