It possible to obtain a solid ester after standard esterification of a solid compound e.g. e p-nitro benzoic acid is solid when you esterified with ethanol using acid catalyst then p-nitro ethyl benzoate obtained is also solid.
Yes it is possible. Assume that you reacted salicylic acid (which is a solid with some acidic strength) with liquid methanol using sulfuric acid as a catalyst, then the main product, after refluxing , will be methyl salicylate (which is a solid ester).