I would say no to both copying and casting Wizard spells above level 1, based on the spellcasting rules under multiclassing on pg 164 of the PHB:
You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class
I read that as saying that you would count as a level 1 wizard, which comes into play under the and can prepare section. A level 1 wizard cannot prepare spells higher than first level. Nor would they be able to scribe them, as spells you are allowed to know are also based on individual single class.
PHB Example with wizard on pg 164 as well:
As a 3rd level wizard, you know three wizard cantrips, and your spellbook contains ten wizards spells, two of which can be 2nd level
The first errata to the PHB clarifies this explicitly:
Your Spellbook (p. 114). The spells copied into a spellbook must be of a spell level the wizard can prepare.
But, you would be able to cast a level 1 wizard spell as a 9th level spell slot, per PHB rules further below:
If you have more than one spellcasting class, this table might give you spell slots of a level that is higher than the spells you know or can prepare. You can use those slots, but only to cast your lower level spells. If a lower level spell that you cast, like burning hands, has an enhanced effect when cast using a higher-level slot, you can use the enhanced effect, even though you don't have any spells of that higher level.
The published rules don't go into this level of detail. As far as I see it there are two basic ways to rule this.
The pragmatic approach
Fine inks are rare, and rare inks are fine. They cost about the same, so they are the same.
The flavourful approach
For example: A wizard's fine inks are the sort you could use to write an invitation to a society ball. They are expensive and durable. A warlock's rare inks dripped from some eldrich rift in reality and are unsuitable for any other purpose than recording a warlock's spells.
Best Answer
Probably Not
This is because the shopkeeper sells items at 10x increased cost, but the wizard is not explicitly buying an item. The PHB (pg. 114) simply states:
Another way to look at it is that "fine inks" are never listed on the shopkeeper page. Remember that the cost is also for "material components". My assumption is that it is intended to be an abstraction for the value of materials the wizard has to expend, rather than an actual price they pay.
Of course, it's up to the DM as always - if they want to bump the price up, then they can.
Also remember that the cost is only for spells found in scrolls, etc. and not for the spells a wizard learns each level.