Its not possible to make the antenna smaller without adversly affecting the range.Depends on how far you want to transmit.
actually you are in luck. since it's 900MHz, you'll find planty of different antennas on ebay. just look for GSM antennas (yes - for cell phones).it all dependes on your transmitter's output power, but i'd imagine that you could easily install tiny antenna on your RC car, and compensate for weeker signal by using higher gain antenna with your reciever.that's how people usually do fpv - small stuff in the air/field/whatever and high gain antenna (usually directional btw) next to the monitor
if you really want to build your antennas, then that's how i would do it:wire antenna for the car:1/2 or 1/4 wave lenght. your wave lenght is ~333.333mm so the antenna would be 166.666mm (1/2 wave) or 83.333mm (1/4 wave). use copper wire and keep it as straight as possible. curved antenna won't perform too well, but might work for you on short distances.if you want high gain directional antenna for your reciever:bi-quad design is probably the simplest to build. you can calculate dimensions here: http://www.changpuak.ch/electronics/bi_quad_antenna_designer.php
any not coductive adhesive should do. i usually use simple hot glue for that stuff1mm should be fine
i would use a wire with insulation on it. this way you won't have to worry about it. 1 - 1.5 mm^2 copper wire should be riggid enough to keep it's shape on it's own anyways.in any case any plastic/rubber will do (as long as it's not coductive)