Hi,
HikaShop 3 do not officially support Joomla 1.5 but it should continue to work.
But, HikaShop 2.6.4 is still compatible with Joomla 1.5.
And yes, we created that plugin a very long time ago when there was no captcha plugin in Joomla.
Regarding the conflict with AcyMailing, I suppose that it's because both captchas use the same div id.
If you edit the file plugins/system/recaptcha2/recaptcha2.php you have that code:
<div id="g-recaptcha" class="g-recaptcha"></div>
<script type="text/javascript">
grecaptcha.render(\'g-recaptcha\', {\'sitekey\':\''.$pubkey.'\', \'theme\':\''.$theme.'\'});
</script>
try changing g-recaptcha to something else and that should help.
Otherwise, please provide a link to the page so that we can have a look.