Disclaimer: I am not a lawyer nor do I have any other official capacity, so please take everything here with a grain of salt. All the following translations are mine, not in any way official or binding.
Permanent Residency
Foreign nationals that have proven Czech origins, may apply for a permanent residence permit for reasons worthy of consideration …, without meeting the condition of prior continuous residence in the Czech Republic. The spouse or minor child of the given foreign national may also apply for the same kind of residence permit.
(Source: Ministry of the Interior)
You may thus be eligible to apply for permanent residency based on your Czech ancestry. Of course, you will have to make your reasons convincing enough (explain your motivation, your potential contribution to the Czech economy, etc.).
Citizenship
First of all, Czech citizenship does not depend on the place of birth at all (the only exception being when a child of two stateless persons is born on Czech soil).
Your own Czech citizenship is determined by § 8 clause 4 of the Act No. 39/1969 Sb.:
A child, whose one parent is a foreign national, acquires (Czech) citizenship by birth if its other parent is a (Czech) citizen.
It thus all depends on your mother, whose Czech citizenship would arise from § 1 clause 2 of the Act No. 194/1949 Sb.:
A child born abroad, whose one parent is a (Czechoslovak) citizen, acquires (Czechoslovak) citizenship upon approval by a Regional National Council (KNV) on request of the parent who is a (Czechoslovak) citizen. The request for approval can be filed within one year of birth.
Your grandfather would thus have to:
- be a Czechoslovak citizen himself AND
- file the application for your mothers citizenship in Czechoslovakia in time AND
- have the application approved
Even then, your mother's citizenship would not be 100% certain, as the mentioned Act contained a provision allowing the Czechoslovak authorities to unilaterally revoke the citizenship of dual citizens living abroad.