Do I need to install the latest Forms patchYes. Check note 1292919.1 "How to Install Oracle Developer Suite 10g (10.1.2) on Windows 7 (32-bit)".
But shouldn't have been receiving an error? That unable to open/find the file.. or something. There is no FRM error in the message lineYes, you would expect this but unfortunately you don't. As InoL indicated, you can look at the MOS Doc ID: 1292919.1, but if you don't have a My Oracle Support account, take a look at an article I wrote: Forms: How to Configure Forms Builder to run forms locally. If you don't want to modify your FORMS_PATH in the default.env, then you would need to create a configuration in the formsweb.cfg that explicitely identifies your form binary and the path to it (eg: form=\<your directory>\form_name.fmx). I found it a lot easier to simply create a directory where I place all of my Forms (.fmb). I then added this directory to the FORMS_PATH and never have to create a configuration specific to run a form. :)
Do I need to install the latest Forms patchTechnically, yes if you want/need a supported (certified) environment. However, if you do not have a My Oracle Support (MOS) account, you can't get the patch. I have the Oracle Developer Suite (ODS) 10g R2 (10.1.2.0.0) installed and running just fine on Windows 7 Professional (64-bit).
And once I can run my form, and asks me to re-enter the password (because of that sensitive password), I think the installation it's ok.So, you're connecting to an Oracle 11g RDBMS? You can either turn off the Case Sensitive passwords on your database or you can add the FORMS_USERNAME_CASESENSITIVE = 1 parameter to your default.env. For more details on this, look at MOS Doc ID: 469013.1 [FRM-41214 and REP-501 when connecting ot Database 11g using RUN_REPORT_OBJECT].